(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[    707152,      13737]
NotebookOptionsPosition[    693722,      13327]
NotebookOutlinePosition[    694267,      13348]
CellTagsIndexPosition[    694224,      13345]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Quantum Particle in a Box ", "Title",
 CellChangeTimes->{{3.472162146123662*^9, 3.4721621604241257`*^9}, {
   3.4726734841923733`*^9, 3.472673484539587*^9}, 3.5710918705215187`*^9}],

Cell[TextData[{
 StyleBox["A little paradox, traced to a failure of hermiticity", 
  "Subsubtitle",
  FontSlant->"Italic"],
 StyleBox["\n", "Subsubtitle"]
}], "Text",
 CellChangeTimes->{{3.571092411435142*^9, 3.5710924286491623`*^9}, {
   3.5710924873416653`*^9, 3.571092514320097*^9}, 3.571092548198052*^9}],

Cell["\<\
Nicholas Wheeler
10 January 2010
Revised 16 January, in response to some observations by David Griffiths, \
Darrell Schroeder & Joel Franklin 

\
\>", "Text",
 CellChangeTimes->{{3.472162166187393*^9, 3.47216218171863*^9}, {
  3.472673378816163*^9, 3.472673379712291*^9}, {3.472673495184366*^9, 
  3.472673505903164*^9}, {3.4726735434288073`*^9, 3.472673605777493*^9}, {
  3.571092584215043*^9, 3.571092604091201*^9}},
 FontSize->10],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.472162185185794*^9}],

Cell[CellGroupData[{

Cell["Introduction", "Subsection",
 CellChangeTimes->{{3.4721622161640253`*^9, 3.472162220058502*^9}}],

Cell[TextData[{
 "A quantum particle of mass ",
 StyleBox["m",
  FontSlant->"Italic"],
 " moves on the interval 0 < ",
 StyleBox["x",
  FontSlant->"Italic"],
 " < ",
 StyleBox["a",
  FontSlant->"Italic"],
 ". The Hamiltonian opearator is standardly taken to have the form "
}], "Text",
 CellChangeTimes->{{3.472162226761022*^9, 3.472162304179789*^9}, {
  3.4726736258946943`*^9, 3.472673634187739*^9}, {3.472673773546467*^9, 
  3.47267378140524*^9}}],

Cell[BoxData[
 RowBox[{"H", "=", 
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{
    SubscriptBox["\[PartialD]", 
     RowBox[{"x", ",", "x"}]], "\[Placeholder]"}]}]}]], "Output"],

Cell["\<\
As a matter of computational (mainly graphic) convenience I set a = 1. The \
normalized energy-eigenstates are\
\>", "Text",
 CellChangeTimes->{{3.472162398450158*^9, 3.472162424455153*^9}, {
  3.472673797086795*^9, 3.472673873142581*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"e", "[", 
   RowBox[{"x_", ",", "n_"}], "]"}], ":=", 
  RowBox[{
   SqrtBox["2"], 
   RowBox[{"Sin", "[", 
    RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{
     SubsuperscriptBox["\[Integral]", "0", "1"], 
     RowBox[{
      RowBox[{"e", "[", 
       RowBox[{"x", ",", "m"}], "]"}], 
      RowBox[{"e", "[", 
       RowBox[{"x", ",", "n"}], "]"}], 
      RowBox[{"\[DifferentialD]", "x"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"m", ",", "1", ",", "4"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "1", ",", "4"}], "}"}]}], "]"}], "//", 
  "TableForm"}]}], "Input",
 CellChangeTimes->{{3.472162473299405*^9, 3.472162473874448*^9}, {
  3.472673883070263*^9, 3.472673910977353*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"1", "0", "0", "0"},
    {"0", "1", "0", "0"},
    {"0", "0", "1", "0"},
    {"0", "0", "0", "1"}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.472162481676373*^9, 3.4726739471313*^9, 
  3.4729990089749193`*^9, 3.571083075857573*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "1"}], "]"}], ",", 
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "2"}], "]"}], ",", " ", 
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "3"}], "]"}], ",", 
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "4"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"Ticks", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", "1", "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", 
         SqrtBox["2"]}], ",", 
        SqrtBox["2"]}], "}"}]}], "}"}]}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "2"}], ",", "2"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4721625236970997`*^9, 3.472162533033746*^9}, {
  3.4721625760597277`*^9, 3.472162582656526*^9}, {3.4726739578514633`*^9, 
  3.4726739690174007`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwV2Hk4VGscB3BKpRQRiUohkrRJWsi3Qou42ZduIdmSa61ESgqhQpIoy1Ru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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwVl3k8lN8Xx5E2W1GJaEELpahIlhxlF8mubGVLVEqKvipZk2zZsu+VyJI9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     "]]}, 
   {Hue[0.1421359549995791, 0.6, 0.6], LineBox[CompressedData["
1:eJwdmgk0lN//x2lPpawlZKmkRalvEck7S2lREdJiCSmEZEso2UnRYs8WRVpQ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     "]]}, 
   {Hue[0.37820393249936934`, 0.6, 0.6], LineBox[CompressedData["
1:eJwVmAk4VO8XxxWVkGwJrUpF2ULKeiRZIlmLLClKi51KlpAliSh+WbIVIRTJ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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-2, 2}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic},
  Ticks->{{{1, 
      FormBox["1", TraditionalForm]}}, {{
      NCache[-2^Rational[1, 2], -1.4142135623730951`], 
      FormBox[
       RowBox[{"-", 
         SqrtBox["2"]}], TraditionalForm]}, {
      NCache[2^Rational[1, 2], 1.4142135623730951`], 
      FormBox[
       SqrtBox["2"], TraditionalForm]}}}]], "Output",
 CellChangeTimes->{3.472162587238109*^9, 3.472673975496573*^9, 
  3.472999022909295*^9, 3.571083076817893*^9}]
}, Open  ]],

Cell["From", "Text",
 CellChangeTimes->{{3.472162847301806*^9, 3.4721628479356203`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[ScriptCapitalE]", "=", 
   FractionBox[
    RowBox[{
     SuperscriptBox["\[Pi]", "2"], " ", 
     SuperscriptBox["\[HBar]", "2"], " "}], 
    RowBox[{"2", " ", "m"}]]}], ";"}]], "Input",
 CellChangeTimes->{{3.472162672635231*^9, 3.472162686079008*^9}, {
  3.472674001834708*^9, 3.472674002829256*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "1"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], "\[Equal]", 
  RowBox[{"\[ScriptCapitalE]", " ", 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "1"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "2"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], "\[Equal]", 
  RowBox[{
   SuperscriptBox["2", "2"], "\[ScriptCapitalE]", " ", 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "3"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], "\[Equal]", 
  RowBox[{
   SuperscriptBox["3", "2"], "\[ScriptCapitalE]", " ", 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "3"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "4"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], "\[Equal]", 
  RowBox[{
   SuperscriptBox["4", "2"], "\[ScriptCapitalE]", " ", 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "4"}], "]"}]}]}]}], "Input",
 CellChangeTimes->{{3.47216271696736*^9, 3.472162795116796*^9}, 
   3.4721628286237583`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.472162804162627*^9, 3.472162830404942*^9}, 
   3.472674016833312*^9, 3.472999040327167*^9, 3.5710830773671494`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.472162804162627*^9, 3.472162830404942*^9}, 
   3.472674016833312*^9, 3.472999040327167*^9, 3.5710830774001083`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.472162804162627*^9, 3.472162830404942*^9}, 
   3.472674016833312*^9, 3.472999040327167*^9, 3.5710830774212093`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.472162804162627*^9, 3.472162830404942*^9}, 
   3.472674016833312*^9, 3.472999040327167*^9, 3.571083077444038*^9}]
}, Open  ]],

Cell[TextData[{
 "we see that the ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["n", "th"], TraditionalForm]]],
 " energy eigenvalue is given by"
}], "Text",
 CellChangeTimes->{{3.472162853731667*^9, 3.472162883036525*^9}, {
  3.472674029350687*^9, 3.4726740306060762`*^9}}],

Cell[BoxData[
 RowBox[{
  SubscriptBox["\[ScriptCapitalE]", "n"], "=", 
  RowBox[{"\[ScriptCapitalE]", " ", 
   SuperscriptBox["n", "2"]}]}]], "Output",
 CellChangeTimes->{{3.472162909773333*^9, 3.472162923786149*^9}}],

Cell["\<\
The paradoxical results that are the point of this discussion emerge when we \
assume the (momentary initial) state of the system to have the simple form of \
the following\[Ellipsis] \
\>", "Text",
 CellChangeTimes->{{3.472674050564641*^9, 3.472674106427698*^9}, {
  3.472674170324175*^9, 3.472674250459311*^9}, {3.4729990787417727`*^9, 
  3.472999091834268*^9}}],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.472162972842368*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Parabolic test state", "Subsection",
 CellChangeTimes->{{3.472185114641535*^9, 3.472185118418091*^9}, {
  3.472185152935001*^9, 3.472185184670282*^9}}],

Cell["We declare an interest in the polynomial state", "Text",
 CellChangeTimes->{{3.472162978979195*^9, 3.472162988462617*^9}, {
  3.47299910524687*^9, 3.472999105502627*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Psi]", "[", "x_", "]"}], ":=", 
  RowBox[{
   SqrtBox["30"], " ", "x", 
   RowBox[{"(", 
    RowBox[{"1", "-", "x"}], ")"}]}]}]], "Input",
 CellChangeTimes->{{3.472163001129842*^9, 3.472163018951026*^9}, {
  3.472163059073659*^9, 3.472163074731799*^9}, {3.472163191850871*^9, 
  3.4721631939403343`*^9}, {3.472674136763496*^9, 3.4726741515677547`*^9}}],

Cell["which is seen to be normalized: ", "Text",
 CellChangeTimes->{{3.472163298443656*^9, 3.472163306228348*^9}, {
  3.472999136703615*^9, 3.472999144795973*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SubsuperscriptBox["\[Integral]", "0", "1"], 
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "x", "]"}], "2"], 
   RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input",
 CellChangeTimes->{
  3.472163285262019*^9, {3.472674264723522*^9, 3.472674270312552*^9}}],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{3.472163286588049*^9, 3.472674274866014*^9, 
  3.4729991498918447`*^9, 3.571083077922756*^9}]
}, Open  ]],

Cell["\<\
I use a graphic technique to compare the parabolic state to the ground state:\
\
\>", "Text",
 CellChangeTimes->{{3.472185260110352*^9, 3.47218527930335*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "1"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"Ticks", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        FractionBox["1", "2"], ",", "1"}], "}"}], ",", 
      RowBox[{"{", 
       SqrtBox["2"], "}"}]}], "}"}]}], ",", " ", 
   RowBox[{"GridLines", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", "0.5", "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        SqrtBox[
         RowBox[{"15", "/", "8"}]], ",", 
        SqrtBox["2"]}], "}"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472163448287881*^9, 3.472163456868244*^9}, {
  3.472163530283551*^9, 3.4721635829517717`*^9}, {3.472163619697864*^9, 
  3.47216362002669*^9}, {3.4721636544562693`*^9, 3.4721636693011723`*^9}, {
  3.472163820957542*^9, 3.472163844176629*^9}, {3.472163892762401*^9, 
  3.47216390414174*^9}, {3.472164211493907*^9, 3.472164227095879*^9}, {
  3.472674306315365*^9, 3.472674336039116*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwdmHk4Vd8Xxo0RRRNFCYlolDSXV6mkUiShQqkkSRkaUElRqGhAhMypyFCa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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV2Hk4VGscB3BKpRQRiUohkrRJWsi3Qou42ZduIdmSa61ESgqhQpIoy1Ru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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  GridLines->
   NCache[{{0.5}, {
     Rational[1, 2] Rational[15, 2]^Rational[1, 2], 2^Rational[1, 2]}}, {{
     0.5}, {1.3693063937629153`, 1.4142135623730951`}}],
  PlotRange->{{0, 1}, {0., 1.4142135210332178`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{{{
      NCache[
       Rational[1, 2], 0.5], 
      FormBox[
       FractionBox["1", "2"], TraditionalForm]}, {1, 
      FormBox["1", TraditionalForm]}}, {{
      NCache[2^Rational[1, 2], 1.4142135623730951`], 
      FormBox[
       SqrtBox["2"], TraditionalForm]}}}]], "Output",
 CellChangeTimes->{
  3.472163551602777*^9, 3.472163623279105*^9, 3.47216367063935*^9, 
   3.472163913116304*^9, {3.472164214452631*^9, 3.472164228180698*^9}, 
   3.4726743400760717`*^9, 3.47299916146579*^9, 3.5710830781646442`*^9}]
}, Open  ]],

Cell[TextData[{
 "In constructing the figure I have taken note of the fact that ",
 StyleBox["\[Psi][x]", "Output"],
 " is maximal at x = 1/2, where it assumes the value"
}], "Text",
 CellChangeTimes->{{3.472163974868142*^9, 3.4721640253491507`*^9}, {
  3.4721642508507643`*^9, 3.472164315654923*^9}, {3.472674359798584*^9, 
  3.472674386845414*^9}, {3.47267442742284*^9, 3.472674432917486*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Psi]", "[", 
   FractionBox["1", "2"], "]"}], "\[Equal]", 
  SqrtBox[
   RowBox[{"15", "/", "8"}]]}]], "Input",
 CellChangeTimes->{{3.472674467924243*^9, 3.472674500677617*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.472674464317217*^9, 3.472674501956586*^9}, 
   3.571083078840912*^9}]
}, Open  ]],

Cell["\<\
The figure establishes that the ground state is by itself a good \
approximation to \[Psi]. 

Fourier analysis enables us to improve upon the approximation:\
\>", "Text",
 CellChangeTimes->{{3.47216485011283*^9, 3.4721649222355843`*^9}, {
  3.4721852999170647`*^9, 3.472185300109625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", 
       RowBox[{
        SubsuperscriptBox["\[Integral]", "0", "1"], 
        RowBox[{
         RowBox[{"\[Psi]", "[", "x", "]"}], 
         RowBox[{"e", "[", 
          RowBox[{"x", ",", "n"}], "]"}], 
         RowBox[{"\[DifferentialD]", "x"}]}]}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n", ",", "1", ",", "13"}], "}"}]}], "]"}], "//", "Simplify"}], 
  "//", "TableForm"}]], "Input",
 CellChangeTimes->{{3.472674973953764*^9, 3.4726749788654623`*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"1", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox["15"]}], 
      SuperscriptBox["\[Pi]", "3"]]},
    {"2", "0"},
    {"3", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox[
        FractionBox["5", "3"]]}], 
      RowBox[{"9", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]},
    {"4", "0"},
    {"5", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox[
        FractionBox["3", "5"]]}], 
      RowBox[{"25", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]},
    {"6", "0"},
    {"7", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox["15"]}], 
      RowBox[{"343", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]},
    {"8", "0"},
    {"9", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox[
        FractionBox["5", "3"]]}], 
      RowBox[{"243", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]},
    {"10", "0"},
    {"11", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox["15"]}], 
      RowBox[{"1331", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]},
    {"12", "0"},
    {"13", 
     FractionBox[
      RowBox[{"8", " ", 
       SqrtBox["15"]}], 
      RowBox[{"2197", " ", 
       SuperscriptBox["\[Pi]", "3"]}]]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.4726749880939503`*^9, 3.472999273666027*^9, 
  3.571083106998969*^9}]
}, Open  ]],

Cell["\<\
That\[LongDash]as these results display\[LongDash]only the odd eigenstates \
contribute to the development of \[Psi] is made obvious by an elementary \
symmetry argument. A very simple formula serves to describe the Fourier \
coefficients of odd order:\
\>", "Text",
 CellChangeTimes->{
  3.472675044493863*^9, {3.472675092493472*^9, 3.4726751105742407`*^9}, {
   3.47267514990807*^9, 3.472675159059765*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", 
       RowBox[{
        RowBox[{
         SubsuperscriptBox["\[Integral]", "0", "1"], 
         RowBox[{
          RowBox[{"\[Psi]", "[", "x", "]"}], 
          RowBox[{"e", "[", 
           RowBox[{"x", ",", "n"}], "]"}], 
          RowBox[{"\[DifferentialD]", "x"}]}]}], "-", 
        FractionBox[
         RowBox[{"8", " ", 
          SqrtBox["15"]}], 
         RowBox[{
          SuperscriptBox["\[Pi]", "3"], 
          SuperscriptBox["n", "3"]}]]}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n", ",", "1", ",", "13", ",", "2"}], "}"}]}], "]"}], "//", 
   "Simplify"}], "//", "TableForm"}]], "Input",
 CellChangeTimes->{{3.472165065095594*^9, 3.472165143134284*^9}, {
   3.472165342058189*^9, 3.472165350575817*^9}, {3.472674535459135*^9, 
   3.472674541570669*^9}, {3.472674607373816*^9, 3.472674610506401*^9}, {
   3.472674751550704*^9, 3.4726747882069263`*^9}, 3.472674849653243*^9, {
   3.47267490500308*^9, 3.472674905555881*^9}, 3.472675061921317*^9}],

Cell[BoxData[
 TagBox[GridBox[{
    {"1", "0"},
    {"3", "0"},
    {"5", "0"},
    {"7", "0"},
    {"9", "0"},
    {"11", "0"},
    {"13", "0"}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.472165131833631*^9, 3.472165147343124*^9}, 
   3.472165361129941*^9, 3.472185477002733*^9, 3.4721855887466784`*^9, 
   3.472674569926772*^9, 3.472674613496365*^9, 3.4726748080316563`*^9, 
   3.472674858647566*^9, 3.472674912574153*^9, 3.472675079776209*^9, 
   3.472999302682836*^9, 3.571083109137126*^9}]
}, Open  ]],

Cell["We are led thus to define expansion coefficients", "Text",
 CellChangeTimes->{{3.472165522820037*^9, 3.472165525666668*^9}, {
  3.472260794422271*^9, 3.4722608064821653`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"c", "[", "k_", "]"}], ":=", 
  RowBox[{
   FractionBox["1", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"2", "k"}], "+", "1"}], ")"}], "3"]], 
   FractionBox[
    RowBox[{"8", " ", 
     SqrtBox["15"]}], 
    SuperscriptBox["\[Pi]", "3"]]}]}]], "Input",
 CellChangeTimes->{{3.472186137626004*^9, 3.472186179318109*^9}}],

Cell["which are found to satisfy the normalization condition", "Text",
 CellChangeTimes->{{3.472260821807363*^9, 3.472260825638348*^9}, {
  3.472675265973579*^9, 3.472675267403462*^9}, {3.472675538464785*^9, 
  3.472675575299849*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  SuperscriptBox[
   RowBox[{"c", "[", "k", "]"}], "2"]}]], "Input"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{3.472675556564424*^9, 3.472999320647811*^9, 
  3.571083110947702*^9}]
}, Open  ]],

Cell["\<\
and manage to do so in excellent approximation even when the series is \
severely truncated: \
\>", "Text",
 CellChangeTimes->{{3.4726759691701107`*^9, 3.472675999165503*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"n", ",", 
      RowBox[{"N", "[", 
       RowBox[{
        RowBox[{
         UnderoverscriptBox["\[Sum]", 
          RowBox[{"k", "=", "0"}], "n"], 
         SuperscriptBox[
          RowBox[{"c", "[", "k", "]"}], "2"]}], ",", "12"}], "]"}]}], "}"}], 
    ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}], "//", 
  "TableForm"}]], "Input",
 CellChangeTimes->{3.472676016506404*^9}],

Cell[BoxData[
 TagBox[GridBox[{
    {"0", "0.9985550143640182042462441242`12."},
    {"1", "0.99992477432885224842216489804`12."},
    {"2", "0.99998868184977154558723665766`12."},
    {"3", "0.99999716942734860972041455329`12."},
    {"4", "0.99999904838477636561091650223`12."},
    {"5", "0.99999961204304969857444654508`12."},
    {"6", "0.99999981891989408251800102305`12."},
    {"7", "0.99999990658453183189682828199`12."},
    {"8", "0.99999994795386005065896643423`12."},
    {"9", "0.9999999691789916273004624674`12."},
    {"10", "0.99999998082175922272451356693`12."}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.4726760196525793`*^9, 3.472999339544218*^9, 
  3.57108311156491*^9}]
}, Open  ]],

Cell["With their aid, we construct", "Text",
 CellChangeTimes->{{3.4726755625372562`*^9, 3.472675567666388*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  RowBox[{
   RowBox[{"c", "[", "k", "]"}], 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", 
     RowBox[{
      RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.4726762919917393`*^9, 3.472676304858891*^9}}],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{
   FractionBox["1", 
    SuperscriptBox["\[Pi]", "3"]], 
   RowBox[{"\[ImaginaryI]", " ", 
    SqrtBox[
     FractionBox["15", "2"]], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Pi]", " ", "x"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"LerchPhi", "[", 
        RowBox[{
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           RowBox[{"-", "2"}], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", 
           "x"}]], ",", "3", ",", 
         FractionBox["1", "2"]}], "]"}]}], "+", 
      RowBox[{
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "x"}]], " ", 
       RowBox[{"LerchPhi", "[", 
        RowBox[{
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "x"}]], ",", 
         "3", ",", 
         FractionBox["1", "2"]}], "]"}]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{3.472186369401176*^9, 3.472675298699925*^9, 
  3.472676324709058*^9, 3.4729993528559713`*^9, 3.571083115543586*^9}]
}, Open  ]],

Cell[TextData[{
 "That function does not look to be real-valued, and certainly does not look \
at all like the simple polynomial ",
 Cell[BoxData[
  RowBox[{
   SqrtBox["30"], "x", 
   RowBox[{"(", 
    RowBox[{"1", "-", "x"}], ")"}]}]],
  CellChangeTimes->{{3.47218656402577*^9, 3.4721865691573973`*^9}}],
 ", but seems on the following graphic evidence to check out:"
}], "Text",
 CellChangeTimes->{
  3.47218649142769*^9, {3.472186582844356*^9, 3.472186608594079*^9}, {
   3.4726753119545813`*^9, 3.472675315147717*^9}, {3.4726754471341*^9, 
   3.47267547018681*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Spectral\[CapitalPsi]", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{"-", 
    FractionBox["1", 
     SuperscriptBox["\[Pi]", "3"]]}], "\[ImaginaryI]", " ", 
   SqrtBox[
    FractionBox["15", "2"]], " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Pi]", " ", "x"}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", 
      RowBox[{"LerchPhi", "[", 
       RowBox[{
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"-", "2"}], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "x"}]],
         ",", "3", ",", 
        FractionBox["1", "2"]}], "]"}]}], "+", 
     RowBox[{
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "x"}]], " ", 
      RowBox[{"LerchPhi", "[", 
       RowBox[{
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "x"}]], ",", 
        "3", ",", 
        FractionBox["1", "2"]}], "]"}]}]}], ")"}]}]}]], "Input",
 CellChangeTimes->{{3.472686170608169*^9, 3.472686205095606*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Plot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
      RowBox[{"Spectral\[CapitalPsi]", "[", "x", "]"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", 
    RowBox[{"Ticks", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", "1", "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"N", "[", 
         SqrtBox[
          RowBox[{"15", "/", "8"}]], "]"}], "}"}]}], "}"}]}], ",", " ", 
    RowBox[{"GridLines", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"N", "[", 
         SqrtBox[
          RowBox[{"15", "/", "8"}]], "]"}], "}"}]}], "}"}]}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.472186388442828*^9, 3.472186421693639*^9}, {
   3.472186650806192*^9, 3.4721866732149677`*^9}, {3.472186728499448*^9, 
   3.472186743977496*^9}, 3.472675330282855*^9, {3.472675366714979*^9, 
   3.472675370812462*^9}, {3.472686227779881*^9, 3.472686231863138*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwdmHk4lN8bxq0RRRtFCYlolbSXW6mkUiShQqlUkrK0oJKiUEghQvY2spQ2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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwdl3k4lF8bx62lhDaJFmRJUUlKq29JSaUIoUJJkqQsJamkUBQipBCylCVL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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  GridLines->{{}, {1.3693063937629153`}},
  PlotRange->{{0, 1}, {0., 1.3693062980419384`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{{{1, 
      FormBox["1", TraditionalForm]}}, {{1.3693063937629153`, 
      FormBox["1.3693063937629153`", TraditionalForm]}}}]], "Output",
 CellChangeTimes->{
  3.472186427704671*^9, {3.472186659829852*^9, 3.4721866775189123`*^9}, {
   3.472186736368775*^9, 3.472186748151781*^9}, 3.4722608601474333`*^9, 
   3.472675390856078*^9, 3.47268624647418*^9, 3.4729994009604683`*^9, 
   3.5710831253817177`*^9}]
}, Open  ]],

Cell["\<\
The preceding Fourier series provides already quite a good-looking \
approximation even when one abandons all but the first few terms:\
\>", "Text",
 CellChangeTimes->{{3.472166800339305*^9, 3.472166823290771*^9}, {
  3.472166992197723*^9, 3.472167019055176*^9}, {3.472675594695656*^9, 
  3.472675596587901*^9}, {3.472686273183572*^9, 3.472686288970832*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
     RowBox[{
      UnderoverscriptBox["\[Sum]", 
       RowBox[{"k", "=", "0"}], "5"], 
      RowBox[{
       RowBox[{"c", "[", "k", "]"}], 
       RowBox[{"e", "[", 
        RowBox[{"x", ",", 
         RowBox[{
          RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", 
   RowBox[{"Ticks", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", "1", "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"N", "[", 
        SqrtBox[
         RowBox[{"15", "/", "8"}]], "]"}], "}"}]}], "}"}]}], ",", " ", 
   RowBox[{"GridLines", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"N", "[", 
        SqrtBox[
         RowBox[{"15", "/", "8"}]], "]"}], "}"}]}], "}"}]}]}], "]"}]], "Input",\

 CellChangeTimes->{{3.472166346706539*^9, 3.472166353501871*^9}, {
  3.4721667209921837`*^9, 3.4721667219247847`*^9}, {3.472166766562481*^9, 
  3.4721667738361397`*^9}, {3.472186806023171*^9, 3.4721868106962337`*^9}, {
  3.4726756301709137`*^9, 3.472675638917878*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwdmHk4Vd8Xxo0RRRNFCYlolDSXV6mkUiShQqkkSRkaUElRqGhAhMypyFCa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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwVmHc4lW0cx60GiSiJpox2vKW8Ld8KaSmk0KItSkiJkpG9yyyr0KJIaRiV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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  GridLines->{{}, {1.3693063937629153`}},
  PlotRange->{{0, 1}, {0., 1.3693063613181182`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{{{1, 
      FormBox["1", TraditionalForm]}}, {{1.3693063937629153`, 
      FormBox["1.3693063937629153`", TraditionalForm]}}}]], "Output",
 CellChangeTimes->{3.472166359151085*^9, 3.472166726439624*^9, 
  3.472166778277309*^9, 3.472186826702196*^9, 3.4722608874513397`*^9, 
  3.4726756468917103`*^9, 3.472999420939982*^9, 3.571083126225245*^9}]
}, Open  ]],

Cell["How good? Look to the difference:", "Text",
 CellChangeTimes->{{3.472675655273658*^9, 3.4726756597841187`*^9}, {
  3.472676064397079*^9, 3.47267606895532*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], "-", 
     RowBox[{
      UnderoverscriptBox["\[Sum]", 
       RowBox[{"k", "=", "0"}], "5"], 
      RowBox[{
       RowBox[{"c", "[", "k", "]"}], 
       RowBox[{"e", "[", 
        RowBox[{"x", ",", 
         RowBox[{
          RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472675688072164*^9, 3.47267569446637*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwcXHc81d8fvkYlFSWEhi0he93ruude49p7ZyRRqYxEKQ0iqYSQJMps+MrK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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-0.0010320240418363325`, 0.001874088989784209}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.472675701221747*^9, 3.472999435946393*^9, 
  3.571083129092834*^9}]
}, Open  ]],

Cell["\<\
Note the occurance of Gibbs phenomenon, which becomes progressively more \
marked (relatively, not absolutely) as the order of the approximation \
increases:\
\>", "Text",
 CellChangeTimes->{{3.4726757280411997`*^9, 3.472675764734799*^9}, {
  3.472676116610634*^9, 3.472676128539064*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], "-", 
     RowBox[{
      UnderoverscriptBox["\[Sum]", 
       RowBox[{"k", "=", "0"}], "20"], 
      RowBox[{
       RowBox[{"c", "[", "k", "]"}], 
       RowBox[{"e", "[", 
        RowBox[{"x", ",", 
         RowBox[{
          RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", ".0002"}], ",", ".0002"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472675779108377*^9, 3.472675872800633*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwcW3c8lW8Ut0JIEsJPJSSVSosSzyVSCWkIDQ1FO6FoGklURkiUVSqzQmWl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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-0.0002, 0.0002}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{
  3.4726757905949583`*^9, {3.472675829248542*^9, 3.472675881497164*^9}, 
   3.472999459072785*^9, 3.5710831390694933`*^9}]
}, Open  ]],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.472261942214769*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Expected value of energy", "Subsection",
 CellChangeTimes->{{3.4723093654703693`*^9, 3.472309375909101*^9}}],

Cell["Let the Hamiltonian", "Text",
 CellChangeTimes->{{3.472309424240963*^9, 3.472309435659069*^9}, 
   3.4723095512715263`*^9}],

Cell[BoxData[
 RowBox[{"H", "=", 
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["\[HBar]", "2"], 
     RowBox[{"2", "m"}]]}], 
   RowBox[{
    SubscriptBox["\[PartialD]", 
     RowBox[{"x", ",", "x"}]], "\[Placeholder]"}]}]}]], "Output"],

Cell["be abbreviated", "Text",
 CellChangeTimes->{{3.472309458963728*^9, 3.4723094649508047`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "\[ScriptCapitalH]"}], 
  RowBox[{
   SubscriptBox["\[PartialD]", 
    RowBox[{"x", ",", "x"}]], "\[Placeholder]"}]}]], "Output",
 CellChangeTimes->{{3.472309524667068*^9, 3.472309543170002*^9}}],

Cell["where evidently ", "Text",
 CellChangeTimes->{{3.472309842092328*^9, 3.47230984585894*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[ScriptCapitalH]", "=", 
   FractionBox[
    SuperscriptBox["\[HBar]", "2"], 
    RowBox[{"2", "m"}]]}], ";"}]], "Input",
 CellChangeTimes->{{3.472309853770537*^9, 3.4723098751922626`*^9}}],

Cell["From", "Text",
 CellChangeTimes->{{3.472309974440855*^9, 3.4723099751595287`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 FractionBox[
  RowBox[{
   RowBox[{"-", "\[ScriptCapitalH]"}], 
   RowBox[{
    SubscriptBox["\[PartialD]", 
     RowBox[{"x", ",", "x"}]], 
    RowBox[{"e", "[", 
     RowBox[{"x", ",", "n"}], "]"}]}]}], 
  RowBox[{"e", "[", 
   RowBox[{"x", ",", "n"}], "]"}]]], "Input",
 CellChangeTimes->{{3.472309599184679*^9, 3.472309666506009*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SuperscriptBox["n", "2"], " ", 
   SuperscriptBox["\[Pi]", "2"], " ", 
   SuperscriptBox["\[HBar]", "2"]}], 
  RowBox[{"2", " ", "m"}]]], "Output",
 CellChangeTimes->{3.4723096395743637`*^9, 3.472309669618321*^9, 
  3.472676625356031*^9, 3.4729995135594387`*^9, 3.571083139687213*^9}]
}, Open  ]],

Cell[TextData[{
 "we recover the information that the ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["n", "th"], TraditionalForm]],
  FormatType->"TraditionalForm"],
 " eigenvalue can be written ",
 Cell[BoxData[
  FormBox[
   RowBox[{"\[ScriptCapitalE]", " ", 
    SuperscriptBox["n", "2"]}], TraditionalForm]],
  FormatType->"TraditionalForm"],
 " with"
}], "Text",
 CellChangeTimes->{{3.472310026837326*^9, 3.4723100801078587`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[ScriptCapitalE]", "==", " ", 
  RowBox[{
   SuperscriptBox["\[Pi]", "2"], " ", "\[ScriptCapitalH]"}]}]], "Input",
 CellChangeTimes->{{3.472309919831896*^9, 3.472309938310624*^9}, {
  3.4726766450335712`*^9, 3.472676645569709*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.472309940855867*^9, 3.4726766592196493`*^9, 
  3.472999526389678*^9, 3.571083139816401*^9}]
}, Open  ]],

Cell["Working directly from ", "Text",
 CellChangeTimes->{{3.472310486461875*^9, 3.472310495010193*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Psi]", "[", 
   RowBox[{"x", ",", "a"}], "]"}], "\[Equal]", 
  RowBox[{
   SqrtBox["30"], " ", "x", " ", 
   RowBox[{"(", 
    RowBox[{"1", "-", "x"}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.4723105696256723`*^9, 3.4723105807081957`*^9}, {
  3.47299955603898*^9, 3.4729995685336637`*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.472310582773779*^9}],

Cell["we get", "Text",
 CellChangeTimes->{{3.472310591147047*^9, 3.4723105921244297`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpectedEnergy", "=", 
  RowBox[{
   SubsuperscriptBox["\[Integral]", "0", "1"], 
   RowBox[{
    RowBox[{"\[Psi]", "[", "x", "]"}], 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "\[ScriptCapitalH]"}], " ", 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], ")"}], 
    RowBox[{"\[DifferentialD]", "x"}]}]}]}]], "Input",
 CellChangeTimes->{{3.472310126436289*^9, 3.472310215358692*^9}, {
  3.472677329435424*^9, 3.472677338112156*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"5", " ", 
   SuperscriptBox["\[HBar]", "2"]}], "m"]], "Output",
 CellChangeTimes->{3.472310223965629*^9, 3.4726773446922703`*^9, 
  3.472999590408537*^9, 3.571083140066753*^9}]
}, Open  ]],

Cell["\<\
If, on the other hand, we display \[Psi] as a weighted superposition of \
energy eigenfunctions (i.e., if we work from the spectral representation of \
\[Psi]) we get\
\>", "Text",
 CellChangeTimes->{{3.472310679861375*^9, 3.472310714129918*^9}, {
  3.4723115818645163`*^9, 3.4723115842548437`*^9}, {3.472999607802902*^9, 
  3.472999625167275*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SpectrallyExpectedEnergy", "=", 
  RowBox[{"\[ScriptCapitalE]", 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "0"}], "\[Infinity]"], 
    RowBox[{
     SuperscriptBox[
      RowBox[{"c", "[", "k", "]"}], "2"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", "k"}], "+", "1"}], ")"}], "2"]}]}]}]}]], "Input",
 CellChangeTimes->{
  3.4726773821309423`*^9, {3.472765407589312*^9, 3.472765416465303*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"5", " ", 
   SuperscriptBox["\[HBar]", "2"]}], "m"]], "Output",
 CellChangeTimes->{3.472310433542325*^9, 3.472677387620241*^9, 
  3.472765422743923*^9, 3.472999636827585*^9, 3.571083140201819*^9}]
}, Open  ]],

Cell["\<\
These results are in perfect agreement:\
\>", "Text",
 CellChangeTimes->{{3.4727654632447233`*^9, 3.472765466423827*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpectedEnergy", "==", "SpectrallyExpectedEnergy"}]], "Input",
 CellChangeTimes->{{3.472765439907617*^9, 3.4727654475740557`*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.472765449510585*^9, 3.4729996462003098`*^9, 
  3.571083140316313*^9}]
}, Open  ]],

Cell["\<\
Had we worked with truncated spectral representations of \[Psi] we would have \
obtained nearly correct results:\
\>", "Text",
 CellChangeTimes->{{3.472310763629251*^9, 3.472310774333887*^9}, {
  3.472677686409724*^9, 3.472677729774179*^9}, {3.4726783306744747`*^9, 
  3.472678330820648*^9}, {3.472765459603139*^9, 3.4727654729224157`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"n", ",", 
      RowBox[{"\[ScriptCapitalE]", " ", 
       RowBox[{"N", "[", 
        RowBox[{
         RowBox[{
          UnderoverscriptBox["\[Sum]", 
           RowBox[{"k", "=", "0"}], "n"], 
          RowBox[{
           SuperscriptBox[
            RowBox[{"c", "[", "k", "]"}], "2"], 
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "k"}], "+", "1"}], ")"}], "2"]}]}], ",", "10"}], 
        "]"}]}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "5", ",", "50", ",", "5"}], "}"}]}], "]"}], "//", 
  "TableForm"}]], "Input",
 CellChangeTimes->{{3.472677454504738*^9, 3.472677561001689*^9}, {
  3.47267759290801*^9, 3.472677650574553*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"5", 
     FractionBox[
      RowBox[{"4.9995311698627189803`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"10", 
     FractionBox[
      RowBox[{"4.9999231865970422177`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"15", 
     FractionBox[
      RowBox[{"4.9999749853524188369`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"20", 
     FractionBox[
      RowBox[{"4.9999889273665519532`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"25", 
     FractionBox[
      RowBox[{"4.9999941634052801509`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"30", 
     FractionBox[
      RowBox[{"4.9999965557900679271`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"35", 
     FractionBox[
      RowBox[{"4.9999978004920515291`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"40", 
     FractionBox[
      RowBox[{"4.999998510913900198`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"45", 
     FractionBox[
      RowBox[{"4.9999989455538076475`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]},
    {"50", 
     FractionBox[
      RowBox[{"4.9999992262395722708`10.", " ", 
       SuperscriptBox["\[HBar]", "2"]}], "m"]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.4726775030631104`*^9, 3.4726775121385117`*^9}, {
   3.4726775558131866`*^9, 3.472677564138567*^9}, {3.4726776028032637`*^9, 
   3.472677652052299*^9}, 3.4729996646318073`*^9, 3.571083140616355*^9}]
}, Open  ]],

Cell["\<\
in which connection we note that the convergence appears to be \
logarithmically (?) slow.\
\>", "Text",
 CellChangeTimes->{{3.472999696020607*^9, 3.472999726699916*^9}}],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.47268694408329*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
DIGRESSION: Comparison of direct and spectral derivative structures\
\>", "Subsection",
 CellChangeTimes->{{3.472686958127111*^9, 3.47268697391429*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"D\[Psi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", "x"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DD\[Psi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DDD\[Psi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "3"}], "}"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{
  3.472686499898203*^9, {3.472686989725245*^9, 3.472686999204009*^9}, {
   3.472687071311522*^9, 3.472687105023663*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"D\[Psi]", ",", "DD\[Psi]", ",", "DDD\[Psi]"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"Red", ",", "Thick"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"Blue", ",", "Thick"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"Green", ",", "Thick"}], "}"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472687008837839*^9, 3.472687023933325*^9}, {
  3.4726871258975*^9, 3.472687236170101*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[1, 0, 0], Thickness[Large], LineBox[CompressedData["
1:eJwt1Ps31GkcwPGhkVuYYZ7aqYYdkVVCJbtWfL67ZORWpFUbk1No2C6Usjld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     "]]}, 
   {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData["
1:eJwLyk9STGVgYGACYhMQbRf68sDFF6leB1RfrL1ktrTfvkWyq81fdAGcP0Wy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     "]]}, 
   {RGBColor[0, 1, 0], Thickness[Large], LineBox[CompressedData["
1:eJxF1HssFHAcAPA7NMo6nR52hJ2ovGKSkkrFIo+aw2R5TUjXC9lKq+naneQR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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-10.954451150103322`, 5.477225351491433}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{{3.472686480098394*^9, 3.472686500930043*^9}, {
   3.472687026219159*^9, 3.4726870365637083`*^9}, 3.4726871445704803`*^9, 
   3.4726872421797132`*^9, 3.472999753342914*^9, 3.571083141164837*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{"DSpectral\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"Spectral\[CapitalPsi]", "[", "x", "]"}], ",", "x"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DDSpectral\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"Spectral\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DDDSpectral\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"Spectral\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "3"}], "}"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.4726866290880013`*^9, 3.4726866598806467`*^9}, {
  3.472687289973262*^9, 3.4726873231141853`*^9}}],

Cell[TextData[{
 "The spectral descriptions of those quite-simple functions are quite \
complicated, so ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " takes a minute or two to construct he following figure:"
}], "Text",
 CellChangeTimes->{{3.472687659307967*^9, 3.4726877389000874`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Fig1", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "DSpectral\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"Red", ",", "Thick"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Fig2", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "DDSpectral\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"Blue", ",", "Thick"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Fig3", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "DDDSpectral\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"Green", ",", "Thick"}], "}"}]}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.472687361048424*^9, 3.4726873844491663`*^9}, {
  3.4726874832039547`*^9, 3.472687490167506*^9}, {3.472687770173979*^9, 
  3.472687915004218*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"Fig1", ",", " ", "Fig2", ",", " ", "Fig3", ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "12"}], ",", "6"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472688042656384*^9, 3.472688055094109*^9}, {
  3.472688098093546*^9, 3.4726881472152*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {RGBColor[1, 0, 0], Thickness[Large], LineBox[CompressedData["
1:eJwllGs01HkcxmeYcstlmF/tVHRG1OqCLdlal+9/l4PcyqWVTZpT0rDVUsrm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      "]]}}, {{}, {}, 
    {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData["
1:eJxFlQtMU3cUxltEwDCLBXwAohZhRkSyEdMFfFwFlIeyxQeLJjw2NnCw6QRq
DESnxeImtKCzMgKK1SFDOihuFMZQIaVBBwVqeQhaWiilLbTlkYmKII6Z63eb
3DS/nO//ne+ce2/uge8TWIk0Gs1m4Ur4/5/guWW9Ko/9rsnHVKli3z6/wDkX
PlsuIrmAELpd3PCnA5fkq0TJvDQkc6CQ5EtE6dSk5OaRwyTnExUOq+2YvweQ
/DMhWRMWw33rSHIe8cfS9LZfyqNJvkzU5Dabxvf7QF+309/V1akD/vXPC4nA
jlOoN9LpGmbNSnCTpjy2LO5LsGxbpyJEV0syn2gWCtMny+7BT2454nE9RUby
FaJl86Llx8LVyPfwWKXT9g+noX/0z9dOz/PnkLfVx2OZeMYG/dqS6766cHo1
6oqqg7VfvGXjfLtFEBwpo5MsJDp9Wzq28BTYlzLYrjprNBh+yvE7M+ZLa5Hv
cX6jJVG+GPtXfdSj0b40w1+lTTvUPhUO7spjtDaMleL+dQdmDHx8vh9+3Xr9
xG+eDOTt4cnE/iFR6N/rLUqSJvORt1dle7s6ehf0T85+oxfvfAF9H4tQ1NVL
MU9f84oaeQAHefrTOOtCT1RA/5T1OFdepYX/0/Y3VxR8K/I+y9xY3J0yC73a
/dE+a68LxQ1J8/a7NmGegWR+gDC1HnXNyrtHWbfCSBYQmr8jQpvitcivjRny
ivc8hbzaubBr2Zkm7HeQ9u5HcdQTx2iLH56PwdKoHK83Isw3+FruMOnkAh7a
m67ebfwA/YaurZcUN9pS9X8L5OKMv8C6vUv6G7Z8C71OpN/OaHSk6i8eiBIi
xODhParDO4qU2N9wgWGZu3ka54et95fcXdsDvT5UuCjsoBT70V8t3Z/0qTtV
N9TcyA4/i3lH2H5bTc5K7Hck+9e+yAEW9CPPNLVHc/zhZwhwE/I+CYLekCV4
uLGiDX6GLvpM55oY7NvoG3jcn1OOvEbuCZ2gdRrzGFVD4pPGFvQzeR/gxNkW
wt/E8c29OPU5+pvkNrekGhf4jbpfny2u5FOcGniIe2Yx+o/KGPRJFxv4jznr
JHF3aNCPpWSW/Miqp+oyZ4GkKA35zKuYbR7Dq/B8mY8zHX7adB9684OIojNB
RvhZGFl+aZFMnLck/kBjbaXeH8u9jC7lZjXYurRqzt6wB37WOL03UVJNcdW5
ooYNdvC3znsy2ZJY1Mcr1Nyb2econj2ZF1+3Ankn9jGKPU2VeN8myuzDXXle
0C9wPLu29/334D9YkVl0
      "]]}}, {{}, {}, 
    {RGBColor[0, 1, 0], Thickness[Large], 
     LineBox[{{0.16318410446916087`, -2.842170943040401*^-14}, {
      0.16346277092346467`, -1.4210854715202004`*^-14}, {
      0.16366154676732425`, -1.4210854715202004`*^-14}, {
      0.16395053626339712`, -4.263256414560601*^-14}, {0.16451781194087337`, 
      1.4210854715202004`*^-14}, {0.1646860068856776, 
      1.4210854715202004`*^-14}, {0.1649306540781202, 
      1.4210854715202004`*^-14}, {
      0.16524257924848448`, -1.4210854715202004`*^-14}}], 
     LineBox[{{0.3445371360261599, 5.684341886080802*^-14}, {
      0.3447658263776925, -1.4210854715202004`*^-14}, {
      0.3450402547995316, -5.684341886080802*^-14}, {
      0.3453253554377756, -2.1316282072803006`*^-14}, {
      0.3457568179010003, -5.684341886080802*^-14}, {
      0.34598550825253294`, -7.105427357601002*^-15}, {
      0.3463162264570331, -7.105427357601002*^-15}, {0.3464154419183833, 
      7.105427357601002*^-15}}], 
     LineBox[{{0.4059894696068307, 2.1316282072803006`*^-14}, {
      0.4063072275480864, 7.105427357601002*^-15}, {0.40647446856979996`, 
      3.552713678800501*^-15}, {0.407043088043626, -7.105427357601002*^-15}, {
      0.4073106736783677, -1.4210854715202004`*^-14}, {
      0.40771205213048023`, -1.7763568394002505`*^-14}, {0.40797963776522195`,
       2.1316282072803006`*^-14}, {0.408314119808649, 0.}, {
      0.40854399422552967`, -7.105427357601002*^-15}, {0.40888552193060934`, 
      0.}}], LineBox[{{0.4480803267398386, 0.}, {0.4483254132416402, 
      3.552713678800501*^-15}, {
      0.4486164534625296, -1.0658141036401503`*^-14}, {
      0.44893812949614426`, -1.7763568394002505`*^-14}, {
      0.44927028535918634`, -7.105427357601002*^-15}, {0.44953601004961996`, 
      0.}}], LineBox[{{0.3354352600351631, -2.842170943040401*^-14}, {
      0.3356182123163892, 2.842170943040401*^-14}, {
      0.33587739471479283`, -4.973799150320701*^-14}, {
      0.3362432992772449, -7.105427357601002*^-15}, {0.33653297372251945`, 
      1.4210854715202004`*^-14}, {
      0.33689887828497156`, -1.4210854715202004`*^-14}, {0.33714281465993967`,
       2.1316282072803006`*^-14}, {
      0.3374324891052143, -1.4210854715202004`*^-14}, {0.3377831476442309, 
      0.}, {0.33805757606607, -3.552713678800501*^-14}, {
      0.3382710203941671, -4.973799150320701*^-14}, {0.33866741700349023`, 
      1.4210854715202004`*^-14}, {
      0.33897233747220035`, -2.842170943040401*^-14}, {
      0.33917053577686196`, -4.263256414560601*^-14}}], 
     LineBox[{{0.3556094080034866, -7.105427357601002*^-15}, {
      0.3559070543875368, 0.}, {0.356155093040912, 
      2.1316282072803006`*^-14}, {
      0.3567999935396869, -4.263256414560601*^-14}, {
      0.3568992090010371, -2.1316282072803006`*^-14}, {0.3571637835646373, 
      0.}}], LineBox[{{0.3961055252235598, 7.105427357601002*^-15}, {
      0.3963563867561301, -7.105427357601002*^-15}, {
      0.3966072482887004, -3.552713678800501*^-14}, {
      0.3969250062299562, -2.1316282072803006`*^-14}, {
      0.397292936477726, -1.4210854715202004`*^-14}, {
      0.3976106944189818, -2.1316282072803006`*^-14}, {
      0.3979451764624089, -7.105427357601002*^-15}, {0.39827965850583597`, 
      7.105427357601002*^-15}, {
      0.39861414054926303`, -1.4210854715202004`*^-14}, {0.39894862259269015`,
       0.}, {0.3991325877165751, -7.105427357601002*^-15}, {
      0.39970120719040114`, 7.105427357601002*^-15}, {0.3999520687229715, 
      7.105427357601002*^-15}, {
      0.4000356892338283, -7.105427357601002*^-15}}], LineBox[CompressedData["

1:eJwLyk9STGVgYGACYlEQbX9r8lwet3VX93xgAAP7WzP0L3qJd9oKwPhz2Uu2
y/zZqwHjL+L3zRNQ28sB46+YcaGkUHKvCIy/dmuQt7D3XiMYf4OiCuM09r0M
MP6OCqHTE3Vs4er3+m+zmDYPYf/+n81+ahm2CjD+yaxzJ1Us90rA+Gf/Tj7T
89YWbv8lttl/9igj9F/fJ+TwnxHh3oectYzP5iPsfzKtr/j3KoR7Xzwp5T0+
D2H+6wC3I15RCPXfF5WvDI1A+Pfv7KiLb+UR6v9lfuM7nACTBwAzKmr7
      "]], 
     LineBox[{{0.0852927271028463, -2.842170943040401*^-14}, {
      0.08554035390369732, 0.}, {
      0.08570543843759805, -2.842170943040401*^-14}, {0.08615116667912978, 
      0.}, {0.08700630456473504, -2.842170943040401*^-14}, {
      0.08705913161558336, -5.684341886080802*^-14}, {
      0.08719119924270397, -2.842170943040401*^-14}, {
      0.08733977532321449, -2.842170943040401*^-14}, {0.08792087288254488, 
      0.}, {0.08831377407322843, 0.}, {0.08851187551390928, 
      2.842170943040401*^-14}}], 
     LineBox[{{0.3298857075046391, -2.842170943040401*^-14}, {
      0.3301296438796072, -2.1316282072803006`*^-14}, {
      0.3304040723014463, -2.1316282072803006`*^-14}, {
      0.3307394848170274, -2.842170943040401*^-14}, {
      0.33104440528573753`, -7.105427357601002*^-15}, {0.33144080189506064`, 
      7.105427357601002*^-15}, {0.33165424622315776`, 
      7.105427357601002*^-15}, {
      0.33189818259812587`, -7.105427357601002*^-15}}], 
     LineBox[{{0.3919746719872351, -4.263256414560601*^-14}, {
      0.39225898172414814`, 7.105427357601002*^-15}, {0.39346311708048576`, 
      2.1316282072803006`*^-14}, {
      0.39471407992290297`, -7.105427357601002*^-15}}], 
     LineBox[{{0.4132728393727867, 7.105427357601002*^-15}, {
      0.41356839219449026`, -3.197442310920451*^-14}, {0.4137818470101651, 
      1.4210854715202004`*^-14}, {
      0.41420300978109265`, -7.105427357601002*^-15}}], 
     LineBox[{{0.45406993758014397`, -1.7763568394002505`*^-15}, {
      0.4542526233048171, -7.105427357601002*^-15}, {
      0.4545183479952507, -5.329070518200751*^-15}, {0.4549169350309012, 
      0.}, {0.45509962075557436`, 8.881784197001252*^-15}, {
      0.45553308415684424`, -1.7763568394002505`*^-15}}], 
     LineBox[{{0.1147076119219685, -7.105427357601002*^-14}, {
      0.11510048426491483`, -1.4210854715202004`*^-14}, {0.11525455185038397`,
       1.4210854715202004`*^-14}, {0.11576297488243215`, 0.}, {
      0.11587082219226053`, -5.684341886080802*^-14}, {0.11622517763883956`, 
      4.263256414560601*^-14}, {0.11648709253413711`, 
      2.842170943040401*^-14}, {0.11659493984396549`, 
      7.815970093361102*^-14}}], 
     LineBox[{{0.4013953587403596, -7.105427357601002*^-15}, {
      0.40164120304227835`, 2.4868995751603507`*^-14}, {
      0.4019589609835341, -1.4210854715202004`*^-14}, {0.40220982251610443`, 
      7.105427357601002*^-15}, {
      0.4026697353258166, -1.7763568394002505`*^-14}, {
      0.4030460276246721, -3.552713678800501*^-14}, {0.4032968891572425, 
      2.1316282072803006`*^-14}, {
      0.40338050966809935`, -2.4868995751603507`*^-14}, {
      0.40415985282928457`, -2.842170943040401*^-14}, {
      0.40445085220706595`, -1.7763568394002505`*^-14}, {
      0.40463481733095086`, -1.0658141036401503`*^-14}, {0.4049525752722066, 
      0.}}], LineBox[{{0.4232543149457645, -1.0658141036401503`*^-14}, {
      0.4234529921203541, 3.552713678800501*^-15}, {
      0.4237485449420577, -3.552713678800501*^-15}, {0.4241590349722015, 
      7.105427357601002*^-15}, {
      0.4244053289902878, -1.7763568394002505`*^-14}, {
      0.4246516230083742, -7.105427357601002*^-15}, {
      0.42514421104454675`, -1.7763568394002505`*^-14}, {0.4253905050626331, 
      7.105427357601002*^-15}, {0.42571889708674815`, 
      3.552713678800501*^-15}, {0.4260144499084518, 
      1.0658141036401503`*^-14}, {
      0.42644135953980133`, -2.842170943040401*^-14}, {0.4267040731590934, 
      1.4210854715202004`*^-14}, {
      0.42701604558200273`, -2.4868995751603507`*^-14}, {
      0.42724017313846113`, -7.105427357601002*^-15}, {0.4277434339154177, 
      1.7763568394002505`*^-14}, {
      0.42805048045796523`, -7.105427357601002*^-15}, {
      0.4283460332796688, -1.4210854715202004`*^-14}, {
      0.4286580057025781, -1.7763568394002505`*^-14}}], 
     LineBox[{{0.46194452270321334`, 5.329070518200751*^-15}, {
      0.4622409718109784, -5.329070518200751*^-15}, {
      0.4625565198808683, -1.0658141036401503`*^-14}, {
      0.4628056367781499, -1.7763568394002505`*^-15}, {0.4632382697897622, 
      0.}, {0.4635695952631466, 1.7763568394002505`*^-15}, {
      0.46388514333303654`, 1.2434497875801753`*^-14}, {
      0.46425051478238283`, -8.881784197001252*^-15}, {
      0.4645494550591207, -8.881784197001252*^-15}, {
      0.46488161092216274`, -1.7763568394002505`*^-15}, {
      0.46519715899205266`, -1.7763568394002505`*^-15}, {
      0.4654761699170081, -5.329070518200751*^-15}}], 
     LineBox[{{0.3477780009209235, -2.842170943040401*^-14}, {
      0.34803596112043367`, 2.842170943040401*^-14}, {
      0.34830053568403385`, -7.105427357601002*^-15}, {0.34863125388853394`, 
      0.}, {0.34896197209303403`, 3.552713678800501*^-14}, {
      0.34917693892595925`, 1.4210854715202004`*^-14}, {
      0.3496564803224843, -7.105427357601002*^-15}, {
      0.3499541267065345, -7.105427357601002*^-15}, {0.35026830900080963`, 
      1.4210854715202004`*^-14}, {0.3506155631155347, 
      7.105427357601002*^-15}, {
      0.35089667358935983`, -2.1316282072803006`*^-14}, {
      0.3512579832277762, -7.105427357601002*^-15}}], 
     LineBox[{{0.45066533998396285`, 1.4210854715202004`*^-14}, {
      0.45093106467439653`, 0.}, {
      0.4512632205374386, -5.329070518200751*^-15}, {
      0.45159537640048064`, -7.105427357601002*^-15}, {
      0.45182788550461006`, -3.552713678800501*^-15}, {0.45227629591971685`, 
      0.}, {0.45259184398960683`, -1.0658141036401503`*^-14}, {
      0.45289078426634466`, -1.0658141036401503`*^-14}}], 
     LineBox[{{0.15462740510759598`, 0.}, {0.15493885585064143`, 
      4.263256414560601*^-14}, {0.15515195372746193`, 
      2.842170943040401*^-14}, {
      0.1551740831223627, -1.4210854715202004`*^-14}, {
      0.1560207373791152, -2.842170943040401*^-14}, {0.15625022740030653`, 
      0.}, {0.15649610956586868`, 4.263256414560601*^-14}, {
      0.1565575801072593, -4.263256414560601*^-14}, {
      0.15747963822811772`, -1.4210854715202004`*^-14}, {0.15756159894997163`,
       0.}, {0.15787304969301708`, 0.}}], 
     LineBox[{{0.17427923491933267`, -5.684341886080802*^-14}, {
      0.1747318322253515, 4.263256414560601*^-14}, {
      0.1747777035739344, -2.842170943040401*^-14}, {
      0.17525170750929195`, -2.842170943040401*^-14}, {0.17538932155504086`, 
      1.4210854715202004`*^-14}, {0.17571042099512177`, 0.}, {
      0.17600093953614734`, -2.842170943040401*^-14}, {
      0.17623947054877884`, -1.4210854715202004`*^-14}, {
      0.1766125575172538, -1.4210854715202004`*^-14}, {0.1768419142601687, 
      2.842170943040401*^-14}, {0.17728533729647095`, 
      2.842170943040401*^-14}, {
      0.1775299844889135, -4.263256414560601*^-14}, {
      0.1778052125804114, -4.263256414560601*^-14}, {0.17810796348105912`, 
      2.842170943040401*^-14}}], 
     LineBox[{{0.35890005413826287`, -2.1316282072803006`*^-14}, {
      0.359214236432538, 7.105427357601002*^-15}, {
      0.3594788109961382, -2.842170943040401*^-14}, {
      0.35985582974926833`, -7.105427357601002*^-15}}], 
     LineBox[{{0.10825988347008489`, -2.842170943040401*^-14}, {
      0.10847557808974168`, -1.4210854715202004`*^-14}, {
      0.10873749298503922`, -5.684341886080802*^-14}, {
      0.10912266194871209`, -2.842170943040401*^-14}, {0.10939998360255654`, 
      4.263256414560601*^-14}, {
      0.10964649173930716`, -1.4210854715202004`*^-14}, {0.10999776583417681`,
       2.842170943040401*^-14}}], 
     LineBox[{{0.4346158870471117, 1.7763568394002505`*^-14}, {
      0.4348456556425506, 7.105427357601002*^-15}, {
      0.43513669586344006`, -1.4210854715202004`*^-14}, {
      0.43532970148360894`, -1.7763568394002505`*^-14}, {0.4357968976276682, 
      1.4210854715202004`*^-14}, {
      0.4360864060579214, -2.842170943040401*^-14}, {0.4363774462788108, 
      1.4210854715202004`*^-14}, {
      0.43668380440606286`, -2.842170943040401*^-14}, {
      0.4369901625333149, -1.7763568394002505`*^-14}, {0.4373271564732921, 
      1.4210854715202004`*^-14}, {
      0.43760287878781895`, -2.842170943040401*^-14}, {
      0.4378939190087084, -1.4210854715202004`*^-14}}], 
     LineBox[{{0.3622775138017206, -4.973799150320701*^-14}, {
      0.3625379543877643, -2.842170943040401*^-14}, {0.3628521366820394, 
      7.105427357601002*^-15}, {
      0.36306710351496463`, -2.842170943040401*^-14}, {0.3635301090012647, 
      4.263256414560601*^-14}, {0.36384429129553986`, 
      5.684341886080802*^-14}, {
      0.36410886585914004`, -3.552713678800501*^-14}, {0.3645057277045401, 
      1.4210854715202004`*^-14}, {
      0.3648364459090402, -1.4210854715202004`*^-14}, {0.36516716411354033`, 
      0.}, {0.3654978823180405, 1.4210854715202004`*^-14}, {
      0.3658616723429906, -7.105427357601002*^-15}, {
      0.3661593187270408, -1.4210854715202004`*^-14}, {0.36649003693154086`, 
      2.842170943040401*^-14}, {
      0.36680421922581596`, -4.263256414560601*^-14}, {0.36708202251759603`, 
      0.}}], LineBox[{{0.11220093230638555`, 2.842170943040401*^-14}, {
      0.11272784344869004`, -1.4210854715202004`*^-14}, {
      0.11278947048287769`, -2.842170943040401*^-14}, {
      0.11314382592945671`, -4.263256414560601*^-14}, {
      0.11340574082475424`, -2.842170943040401*^-14}, {
      0.11362143544441104`, -2.842170943040401*^-14}}], 
     LineBox[{{0.4397627035849458, -1.4210854715202004`*^-14}, {
      0.44005374380583523`, -3.552713678800501*^-15}, {0.4403601019330873, 
      1.0658141036401503`*^-14}, {
      0.4406664600603393, -1.7763568394002505`*^-14}, {0.4408962286557783, 
      2.1316282072803006`*^-14}}], 
     LineBox[{{0.460008884411336, -1.5987211554602254`*^-14}, {
      0.4602646444258782, 1.7763568394002505`*^-15}, {
      0.46056358470261605`, -3.552713678800501*^-15}, {
      0.4609953873245707, -8.881784197001252*^-15}, {0.4612278964287001, 
      1.0658141036401503`*^-14}}], 
     LineBox[{{0.9488183546432605, 5.684341886080802*^-14}, {
      0.9491313704258975, 2.842170943040401*^-14}, {
      0.9491643194556487, -2.842170943040401*^-14}, {
      0.9492582241904389, -2.842170943040401*^-14}, {
      0.949742883824937, -9.237055564881302*^-14}}], 
     LineBox[{{0.1690132041020059, 0.}, {
      0.16927314174397615`, -4.263256414560601*^-14}, {
      0.1695330793859464, -4.263256414560601*^-14}, {
      0.17000708332130396`, -1.4210854715202004`*^-14}, {
      0.17019056871563587`, -4.263256414560601*^-14}, {
      0.1704505063576061, -4.263256414560601*^-14}, {
      0.17048567439151974`, -1.4210854715202004`*^-14}}], 
     LineBox[{{0.3525601861579952, -5.684341886080802*^-14}, {
      0.35279830326523537`, 0.}, {
      0.35293059054703557`, -3.552713678800501*^-14}, {
      0.3532943805719857, -2.1316282072803006`*^-14}, {
      0.35359202695603587`, -3.552713678800501*^-14}, {0.3537243142378361, 
      7.105427357601002*^-15}}], 
     LineBox[{{0.1459453058415945, -1.4210854715202004`*^-14}, {
      0.1459723528798063, 4.263256414560601*^-14}, {0.14608709789040186`, 
      0.}, {0.14641494077781814`, 1.4210854715202004`*^-14}, {
      0.1466772150877511, 1.4210854715202004`*^-14}, {
      0.14707062655265069`, -2.842170943040401*^-14}, {
      0.14738207729569613`, -1.4210854715202004`*^-14}, {
      0.1477091005758939, -8.526512829121202*^-14}}], 
     LineBox[{{0.4426279179700705, 1.4210854715202004`*^-14}, {
      0.4428569206701914, -1.4210854715202004`*^-14}, {
      0.4431173250783556, -3.552713678800501*^-15}, {
      0.4433624115801572, -7.105427357601002*^-15}}], 
     LineBox[{{0.09982016608610483, 2.842170943040401*^-14}, {
      0.1000677928869558, -2.842170943040401*^-14}, {0.10039796195475713`, 
      2.842170943040401*^-14}, {0.10066209720899821`, 0.}}], 
     LineBox[{{0.1196215975605068, -1.4210854715202004`*^-14}, {
      0.11992279969009899`, 2.842170943040401*^-14}, {
      0.12018471458539653`, -5.684341886080802*^-14}, {
      0.12024634161958417`, -1.4210854715202004`*^-14}}], 
     LineBox[{{0.18184800743552512`, 1.4210854715202004`*^-14}, {
      0.18193363395288015`, 1.4210854715202004`*^-14}, {
      0.18211711934721206`, -4.263256414560601*^-14}, {0.18236176653965464`, 
      1.4210854715202004`*^-14}}], 
     LineBox[{{0.38729192337925566`, -1.4210854715202004`*^-14}, {
      0.38757623311616873`, -1.4210854715202004`*^-14}, {
      0.38787726695525315`, -7.105427357601002*^-15}, {
      0.38815321464108044`, -2.842170943040401*^-14}}], 
     LineBox[{{0.4113189068293019, 1.0658141036401503`*^-14}, {
      0.4115980400497998, -2.4868995751603507`*^-14}, {0.4118443340678862, 
      1.0658141036401503`*^-14}, {0.4121727260920012, 
      7.105427357601002*^-15}}], 
     LineBox[{{0.3281476608329914, -1.4210854715202004`*^-14}, {
      0.3283001210673465, -1.4210854715202004`*^-14}, {0.32855930346575013`, 
      0.}, {0.3288047644430617, 2.1316282072803006`*^-14}}], 
     LineBox[{{0.4309732889140849, -1.7763568394002505`*^-14}, {
      0.4312306297409767, -7.105427357601002*^-15}, {
      0.43147571624277825`, -7.105427357601002*^-15}, {0.4316442132127668, 
      1.0658141036401503`*^-14}}], 
     LineBox[{{0.4666918603757419, -3.552713678800501*^-15}, {
      0.46687454610041507`, -7.105427357601002*^-15}, {0.46715687858400085`, 
      7.105427357601002*^-15}, {
      0.4672523733946252, -3.552713678800501*^-15}}], 
     LineBox[{{0.10562532775856256`, -2.842170943040401*^-14}, {
      0.10570236155129711`, -5.684341886080802*^-14}, {
      0.1059180561709539, -2.842170943040401*^-14}, {0.10609831524595283`, 
      1.4210854715202004`*^-14}}], 
     LineBox[{{0.3402103145751634, 0.}, {0.3405579239094929, 
      1.4210854715202004`*^-14}, {0.340801860284461, 
      2.1316282072803006`*^-14}, {
      0.34093907449538063`, -7.105427357601002*^-15}}], 
     LineBox[{{0.9627337406194999, -9.237055564881302*^-14}, {
      0.9629689447659968, 2.842170943040401*^-14}}], 
     LineBox[{{0.9501980952640947, -9.237055564881302*^-14}, {
      0.9504328571010725, 5.684341886080802*^-14}}], 
     LineBox[{{0.9581154725380765, 7.815970093361102*^-14}, {
      0.9583570987562524, 0.}}]}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{-12, 6},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{
  3.472688057830675*^9, {3.47268813914499*^9, 3.472688148627046*^9}, 
   3.571083257924281*^9}]
}, Open  ]],

Cell[TextData[{
 "And the simplest of the functions was evidently posed for ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " the greatest computational challenge (notice how the green curve is \
broken). \n\n",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " has less difficulty if one works in finite approximation;",
 StyleBox[" i.e",
  FontSlant->"Italic"],
 "., with truncated series:"
}], "Text",
 CellChangeTimes->{{3.4726907577006197`*^9, 3.4726908126342583`*^9}, {
  3.47269088704918*^9, 3.4726909021956587`*^9}, {3.472756184992976*^9, 
  3.47275622391049*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"\[CapitalPsi]", "[", "x_", "]"}], ":=", 
  RowBox[{
   UnderoverscriptBox["\[Sum]", 
    RowBox[{"k", "=", "0"}], "10"], 
   RowBox[{
    RowBox[{"c", "[", "k", "]"}], 
    RowBox[{"e", "[", 
     RowBox[{"x", ",", 
      RowBox[{
       RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]", "[", "x", "]"}], ",", "x"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DD\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DDD\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "3"}], "}"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.472756349716503*^9, 3.47275642983642*^9}, {
   3.472756465876617*^9, 3.472756488019814*^9}, 3.472756553550589*^9, {
   3.472756592756819*^9, 3.472756618410266*^9}, {3.472756744139504*^9, 
   3.472756744335491*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"fig1", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "D\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", "Red", "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"fig2", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "DD\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", "Blue", "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"fig3", "=", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"Evaluate", "[", "DDD\[CapitalPsi]", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", "Green", "}"}]}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.472756531998905*^9, 3.4727565361332827`*^9}, {
  3.472756654008795*^9, 3.4727566640853033`*^9}, {3.4727574189775553`*^9, 
  3.472757425247431*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"fig1", ",", " ", "fig2", ",", "fig3", ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "12"}], ",", "6"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472756699750593*^9, 3.47275670505595*^9}, {
  3.472756842691016*^9, 3.472756847524856*^9}, {3.472757679064332*^9, 
  3.4727576827729187`*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJwt1nkw1tsfB3Bb4Sfb4znqqZC1CEnSdvM5WVpQXUKUJVuWkihECl1Ki6Vy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      "]]}}, {{}, {}, 
    {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJwUm3c81V8YxzWIFMouDdzvRalUssIjO7sQCpGVsiOKQqTIKiUyInuPbNKx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      "]]}}, {{}, {}, 
    {RGBColor[0, 1, 0], LineBox[CompressedData["
1:eJwUV3c8lt8bNlJKSUiIkuxs77DvY++RTRKSiIZRlISGVCpJQkKFkLJH5rH3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      "]]}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{-12, 6},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.472756711053976*^9, 3.4727567615653973`*^9, 
  3.472756848963728*^9, 3.472757440992498*^9, 3.47275768455709*^9, 
  3.4730011202619047`*^9, 3.5710832588809853`*^9}]
}, Open  ]],

Cell["\<\
But, as the figure illustrates, truncation leads to imprecisions that become \
rapidly more conspicuous as the order of the differentiation increases. I \
increase the number of terms in the truncated series, and look in finer \
detail to the results:\
\>", "Text",
 CellChangeTimes->{{3.472757489071827*^9, 3.472757619829095*^9}, {
  3.47300113434414*^9, 3.473001138115446*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"\[CapitalPsi]\[CapitalPsi]", "[", "x_", "]"}], ":=", 
  RowBox[{
   UnderoverscriptBox["\[Sum]", 
    RowBox[{"k", "=", "0"}], "50"], 
   RowBox[{
    RowBox[{"c", "[", "k", "]"}], 
    RowBox[{"e", "[", 
     RowBox[{"x", ",", 
      RowBox[{
       RowBox[{"2", "k"}], "+", "1"}]}], "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D\[CapitalPsi]\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]\[CapitalPsi]", "[", "x", "]"}], ",", "x"}], 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DD\[CapitalPsi]\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DDD\[CapitalPsi]\[CapitalPsi]", "=", 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[CapitalPsi]\[CapitalPsi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "3"}], "}"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.472756349716503*^9, 3.47275642983642*^9}, {
   3.472756465876617*^9, 3.472756488019814*^9}, 3.472756553550589*^9, {
   3.472756592756819*^9, 3.472756618410266*^9}, {3.472756744139504*^9, 
   3.472756744335491*^9}, {3.472756990299258*^9, 3.472757034267685*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", "D\[CapitalPsi]\[CapitalPsi]", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", "Red", "}"}]}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "12"}], ",", "6"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{
  3.472757651746072*^9, {3.472757698997468*^9, 3.4727577084183683`*^9}, {
   3.47275790403506*^9, 3.472757908639598*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJwtlXk41fkex21NcpL1O0XJyKEpihs1lvT5TjLKVoxljK2FrpTGVpbIcDEx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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-12, 6}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{3.472757710306199*^9, 3.4727579101395483`*^9, 
  3.473001167082716*^9, 3.5710832592964478`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", "DD\[CapitalPsi]\[CapitalPsi]", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", "Blue", "}"}]}], ",", " ", 
   RowBox[{"PlotPoints", "\[Rule]", "50"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "13"}], ",", "0"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472757336190585*^9, 3.4727573615674877`*^9}, {
  3.472757741797323*^9, 3.472757760029798*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJwUm3c81W0YxiVlJGkamXGOPUIpqdtKCiUlFJJEy0sILYWShpKVsmfI3ttj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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-13, 0}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{
  3.472757305636046*^9, 3.472757363226369*^9, {3.472757747307979*^9, 
   3.472757762020122*^9}, 3.473001172117963*^9, 3.57108325982907*^9}]
}, Open  ]],

Cell["\<\
Gibbs phenomenon is the dominant feature of the preceding figure. It is even \
more conspicuous in the following figure\
\>", "Text",
 CellChangeTimes->{{3.4727577976684227`*^9, 3.472757847216819*^9}, {
  3.47275816227353*^9, 3.472758194474037*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", "DDD\[CapitalPsi]\[CapitalPsi]", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", "Green", "}"}]}], ",", " ", 
   RowBox[{"PlotPoints", "\[Rule]", "50"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "60"}], ",", "60"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472758098487221*^9, 3.472758100847954*^9}, {
  3.4727581320048523`*^9, 3.472758133954705*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[0, 1, 0], 
    LineBox[{{0.019101995231735596`, 60.}, {
     0.0196286612015304, -2.37160584442357}, {
     0.01996115644971678, -39.49586065687274}, {
     0.020153368658549938`, -60.}}], 
    LineBox[{{0.07621505606179527, 60.}, {0.07660519283474031, 
     50.77272295365604}, {0.07690956416675163, 42.90253087602528}, {
     0.07721393549876293, 34.686994808767665`}, {0.07782267816278556, 
     17.542514955154026`}, {0.07812704949479687, 8.778795784967151}, {
     0.07843142082680818, -0.0013895735522879704`}, {
     0.0790401634908308, -17.280455862088793`}, {
     0.07934453482284212, -25.617873410774955`}, {
     0.07964890615485343, -33.650320160452424`}, {
     0.08025764881887605, -48.510245788766404`}, {
     0.08058781788667738, -55.74539336927139}, {0.08080206928678739, -60.}}], 
    LineBox[CompressedData["
1:eJwcV3k8VO/3J7KTfd+y7+sYu/NYsyWJlCRUSpSSJJUtaZMtRCGpD5IkFVJ4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     "]], 
    LineBox[{{0.009555716032440096, -60.}, {0.009814340804846833, 
     2.372813178183037}, {0.010076034691071763`, 60.}}], 
    LineBox[{{0.06672846867072219, -60.}, {
     0.06686531021037832, -56.22506941722149}, {
     0.06716968154238964, -47.10349120211969}, {
     0.06747405287440095, -37.61728932687599}, {
     0.06808279553842357, -17.92316113190821}, {
     0.06838716687043489, -7.904751453317573}, {0.0686915382024462, 
     2.1010411871276844`}, {0.06930028086646882, 21.699886214394503`}, {
     0.06960465219848014, 31.110883426259583`}, {0.06990902353049144, 
     40.146816391602236`}, {0.07051776619451407, 56.77063879835682}, {
     0.07064988672675312, 60.}}], 
    LineBox[{{0.08568495098877137, -60.}, {
     0.08587052297149865, -56.501117999692596`}, {
     0.08620069203929998, -49.693004362721524`}, {
     0.08686103017490264, -34.65297211024133}, {
     0.08818170644610795, -1.3754828787393123`}, {0.08851187551390928, 
     7.064553939454093}, {0.0888420445817106, 15.364766621954324`}, {
     0.08917221364951194, 23.43392128578956}, {0.08950238271731327, 
     31.184001821199665`}, {0.0898325517851146, 38.53116016989309}, {
     0.09016272085291593, 45.39661390245253}, {0.09049288992071726, 
     51.70748158593719}, {0.09082305898851858, 57.397547181267626`}, {
     0.09099455222279484, 60.}}], LineBox[CompressedData["
1:eJwBgQF+/lJvYiFlAAAAAgAAABcAAAACP7q+Xw2R5pbATgAAAAAAAD+6vojA
C4pYwE383K90HlI/utK6Zobp7sBML3TnQC2mP7rm7A0CSYXASh6TBZYuAD+6
+x2zfakcwEfPuTX4/gY/uw9PWfkIssBFSPs8mJp0P7s3sqbvx9/AP10zPj+2
ez+7S+RNayd2wDlSwoOGSOQ/u2AV8+aHDMAzEezvXIjiP7uIeUDdRjnAGLKf
mK6EAD+7nKrnWKXQP9Xbm+c+egA/u7DcjdQFZkAbRh/oOufwP7vZP9rKxJNA
M2gCpbKMmD+77XGBRiQqQDllgiqCL9w/vAGjJ8GDwEA/G4zr77PuP7wV1M48
41ZAQj4sAQYmWj+8KgZ0uELtQES9f2lbUzg/vD44GzOihEBHBdDeMcqsP7xS
acGvAhpASRHBCTglaz+8ZptoKmGwQErcjZTMiUM/vHrNDqXBR0BMYhwdYSel
P7yO/rUhIN5ATZ8DdSxHij+8lxpQe0+iQE4AAAAAAADHrqjd
     "]], 
    LineBox[{{0.8987448511330249, 60.}, {0.8989366583220757, 
     57.851097099657736`}, {0.8992464409031103, 53.78860856725333}, {
     0.899556223484145, 49.1707793556518}, {0.8998660060651797, 
     44.039801638096485`}, {0.900485571227249, 32.433227797598924`}, {
     0.9007953538082838, 26.06672049736538}, {0.9011051363893184, 
     19.404226973438625`}, {0.9017247015513878, 5.449391216067667}, {
     0.9029638318755265, -23.05964129878759}, {
     0.9032736144565612, -29.902148316561558`}, {
     0.9035833970375959, -36.49195551183389}, {
     0.9038931796186306, -42.762547758652175`}, {
     0.9042029621996652, -48.65013410350143}, {
     0.9045127447807, -54.09429057973638}, {
     0.9048225273617346, -59.038574037060386`}, {0.9048903318468368, -60.}}], 
    LineBox[{{0.9191981962553918, 60.}, {0.9193518585738045, 
     56.996064352641426`}, {0.9196555511355271, 50.4739903566393}, {
     0.9202629362589725, 35.909285464140545`}, {0.9205666288206951, 
     27.9971502245566}, {0.9208703213824178, 19.759648406531895`}, {
     0.921477706505863, 2.613629400414027}, {
     0.9226924767527537, -32.10381348052665}, {
     0.9229961693144764, -40.39132467632114}, {
     0.923299861876199, -48.359506893900004`}, {
     0.9236035544379216, -55.93044169170227}, {0.9237776507906302, -60.}}], 
    LineBox[{{0.9394760750207805, 60.}, {0.9395761517980301, 
     56.96733519048272}, {0.9399056420955427, 46.23665999211875}, {
     0.9402351323930553, 34.8713733828818}, {0.9405646226905681, 
     22.99110337302931}, {0.9412236032855934, -1.8021643329073314`}, {
     0.9425415644756441, -51.6952819946056}, {0.9427750075921252, -60.}}], 
    LineBox[CompressedData["
1:eJwLyk9STGVgYGACYmEQbb8jMqAwR0fEwY8BDID8StPZqU4Ovr93Mb07YWC/
I1+m7ctkCwfv1MxHtvMO2O9o2X/D96Cug0dr7IsHYsfsd8xK1lz2XsnBNcW5
Vmdbm/2ODWzVDLLiDk7cRbyL9u6z33F05ZlIbx4HW855b/t/9Njv+PAhn3vZ
dwedeNluprAe+51skw+kXHnjIGUetyL4Aof9ThlzwX1Mj/Z/nBs38ecuBvud
7rVbCuLOHDBQ4WtZu2mX/c5YRdaTPYcOmMfIZav8vmO/s+hIuNKu7QfsXJf2
RD50sd/Zkb6i+sWaA05pu77/cHtov3Me18+rYosOuBacjtBnv2m/c/M6bz2X
6Qc8LHbV1d+XtN95MnBOe1HPAa/tHNmH44Hm3fvy9sGCpgM+T4W6JmVJ2+98
/eb8H2mxA9DwAQC/PY9c
     "]], LineBox[CompressedData["
1:eJwBUQGu/lJvYiFlAAAAAgAAABQAAAACP+xtIutHvx7ATgAAAAAAAD/sbaWb
+aKkwE3SrzLbNY4/7HBdepcaM8BMiYvxt1LmP+xzFVk0kcLASuvGxE1vnj/s
dc030glSwEj9kP3783M/7HiFFm+A4cBGxAqVA1TNP+x7PPUM+HDAREU0t5wd
oz/sffTTqm//wEGH4cS4K4w/7ICsskfnjsA9J0WlccCsP+yGHG+C1qzAME/A
+nCxFT/skPvp+LTpQCbeK/gevpg/7JOzyJYseEAyWSwoNWvSP+yWa6czpAhA
ORiltr7dED/smSOF0RuXQD+ZuJM+1n0/7JvbZG6TJkBC5JhMvhoyP+yek0MM
CrVARcpT75j14j/soUshqYJEQEh1XoD7Gn0/7KQDAEb500BK3aNtGkWUP+ym
ut7kcWJATPvCfVgtyj/sqENduhb7QE4AAAAAAAANd6HY
     "]], 
    LineBox[{{0.9090061326510508, -60.}, {
     0.9091594834962201, -57.67997020776616}, {
     0.9094692660772548, -52.39235500529185}, {
     0.9097790486582895, -46.55189059016496}, {
     0.9103986138203588, -33.433081847869644`}, {
     0.9107083964013936, -26.27768934974008}, {
     0.9110181789824282, -18.814212503101075`}, {
     0.9116377441444976, -3.2516162415105256`}, {0.9128768744686363, 
     28.278832333533664`}, {0.913186657049671, 35.791753123974836`}, {
     0.9134964396307057, 43.00353801648245}, {0.9138062222117403, 
     49.84102084606029}, {0.914116004792775, 56.234202081896186`}, {
     0.9143143096074771, 60.}}], 
    LineBox[{{0.9293524366793036, -60.}, {
     0.9293737131106521, -59.49610700303214}, {
     0.9299810982340975, -43.300662476758326`}, {
     0.9302847907958202, -34.440792807587776`}, {
     0.9305884833575429, -25.177361397013087`}, {
     0.9311958684809881, -5.780296844206255}, {0.9324106387278788, 
     33.94740568108436}, {0.9327143312896015, 43.52659271176105}, {
     0.9330180238513242, 52.77765038356552}, {0.9332663551547349, 60.}}], 
    LineBox[{{0.9596802428189671, 60.}, {0.9598943807595006, 
     49.04786603953112}, {0.9602018371601502, 32.60195990381079}, {
     0.9608167499614495, -1.8545576431461726`}, {
     0.961124206362099, -19.54809747151525}, {
     0.9614316627627487, -37.33124087704509}, {0.9618281995652673, -60.}}], 
    LineBox[{{0.9798469094927832, 60.}, {0.980093590072267, 
     33.48803936961926}, {0.9807800172970798, -45.00787658260191}, {
     0.980906131164951, -60.}}], 
    LineBox[{{0.9495841305158659, -60.}, {
     0.9497903510209228, -51.90637516736305}, {
     0.9504493316159481, -23.931645629006233`}, {
     0.9507788219134607, -9.181746974822651}, {0.9511083122109735, 
     5.868292833836712}, {0.9517672928059988, 36.211807181329114`}, {
     0.9520967831035115, 51.16934166650489}, {0.9522962167799967, 60.}}], 
    LineBox[{{0.9697676651733056, -60.}, {
     0.9700404419809383, -40.71091907821851}, {0.9706553547822376, 
     5.118260862902652}, {0.9709628111828873, 28.79819170848736}, {
     0.971270267583537, 52.70127096086725}, {0.9713646050026608, 60.}}], 
    LineBox[{{0.047704522489302084`, -60.}, {
     0.04773850681457202, -58.51901915040472}, {
     0.048359429517218694`, -30.39685685571044}, {
     0.04866989086854203, -16.086489214966683`}, {
     0.04898035221986537, -1.798061450126447}, {0.04960127492251203, 
     26.160368613048952`}, {0.04991173627383537, 39.56352393567533}, {
     0.0502221976251587, 52.413509416304166`}, {0.05042201837572795, 60.}}], 
    LineBox[{{0.038172308824529176`, 60.}, {0.038248395099967615`, 
     55.74857759595857}, {0.038580890348154, 36.605587049675066`}, {
     0.038913385596340375`, 17.37655821041964}, {
     0.03957837609271313, -20.485174692349425`}, {
     0.039910871340899504`, -38.70531442803528}, {
     0.04024336658908589, -56.19063050761942}, {
     0.040322404925793545`, -60.}}], 
    LineBox[{{0.05722482592592846, 60.}, {0.0573628087055954, 
     55.1486192558736}, {0.05767327005691873, 43.80684641988184}, {
     0.058294192759565405`, 20.3082854937157}, {0.05860465411088874, 
     8.386594759988277}, {0.05891511546221208, -3.493361318453019}, {
     0.05953603816485875, -26.66775035262672}, {
     0.05984649951618209, -37.7399009939521}, {
     0.060156960867505424`, -48.32783617432552}, {
     0.06053179549992725, -60.}}], 
    LineBox[{{0.9899221752811889, -60.}, {
     0.9900467848320518, -33.512257816245175`}, {0.9903899984444582, 
     45.071956192633635`}, {0.9904511099441136, 60.}}], 
    LineBox[{{0.028635348484637935`, -60.}, {
     0.028938528150749005`, -36.45484488841464}, {
     0.029271023398935385`, -10.756462890047473`}, {0.02960351864712176, 
     14.486873839718328`}, {0.03023315403777339, 60.}}]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-60, 60}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{3.472758105386948*^9, 3.472758137312214*^9, 
  3.473001187234757*^9, 3.571083260537079*^9},
 ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"]]
}, Open  ]],

Cell["\<\
of which this is a 10\[Cross] magnification:\
\>", "Text",
 CellChangeTimes->{{3.4727582036690207`*^9, 3.4727582337999067`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Evaluate", "[", "DDD\[CapitalPsi]\[CapitalPsi]", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", "Green", "}"}]}], ",", " ", 
   RowBox[{"PlotPoints", "\[Rule]", "50"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "600"}], ",", "600"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472757864352662*^9, 3.472757883107127*^9}, {
  3.472757922113064*^9, 3.472758006695283*^9}, {3.47275804000445*^9, 
  3.4727580422552423`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[0, 1, 0], LineBox[CompressedData["
1:eJwUWHc8UN8bRpIdFV8yE2Xvvd5j770lkZUoJUmDIkllZSskOzt7O/bee0SU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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-600, 600}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{
  3.4727578855016737`*^9, {3.472757925177772*^9, 3.4727580085660353`*^9}, 
   3.4727580449305067`*^9, 3.473001205006782*^9, 3.571083261065031*^9}]
}, Open  ]],

Cell[TextData[{
 "If we call that function ",
 StyleBox["f(x)", "Input",
  FontColor->RGBColor[0, 1, 0]],
 StyleBox[" ",
  FontColor->RGBColor[0, 1, 0]],
 StyleBox["then it is only in an approximate (meaning averaged) sense that it \
is the zero function, though we can expect to have  ",
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.472760068186139*^9, 3.472760075716161*^9}, {
  3.4727601328795156`*^9, 3.4727602409052277`*^9}, {3.473001258544696*^9, 
  3.473001262903565*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SubsuperscriptBox["\[Integral]", "0", "1"], 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"slowly", " ", "changing", " ", "funcion"}], ")"}], 
    StyleBox["f", "Input",
     FontColor->RGBColor[0, 1, 0]], 
    StyleBox[
     RowBox[{"(", "x", ")"}], "Input",
     FontColor->RGBColor[0, 1, 0]], 
    RowBox[{"\[DifferentialD]", "x"}]}]}], "\[TildeTilde]", "0"}]], "Output"],

Cell["except possibly for Gibbsian end effects.", "Text",
 CellChangeTimes->{{3.472760316690949*^9, 3.472760352837867*^9}}],

Cell["\<\
The reason one must keep more and more terms to get good approximations to \
exact results emerges when one compares\
\>", "Text",
 CellChangeTimes->{{3.472760593462384*^9, 3.472760633466407*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   FractionBox[
    RowBox[{"8", 
     SqrtBox["30"]}], 
    RowBox[{
     SuperscriptBox["\[Pi]", "3"], 
     SuperscriptBox["n", "3"]}]], 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "x"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "x"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "x"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "x"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "x"}], "]"}]}], "Input",
 CellChangeTimes->{{3.472760642504106*^9, 3.472760664870298*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"16", " ", 
   SqrtBox["15"], " ", 
   RowBox[{"Cos", "[", 
    RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}], 
  RowBox[{
   SuperscriptBox["n", "2"], " ", 
   SuperscriptBox["\[Pi]", "2"]}]]], "Output",
 CellChangeTimes->{3.472760669745635*^9, 3.473001343076909*^9, 
  3.571083261368791*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"16", " ", 
    SqrtBox["15"], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"n", " ", "\[Pi]"}]]}]], "Output",
 CellChangeTimes->{3.472760669745635*^9, 3.473001343076909*^9, 
  3.571083261386932*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "16"}], " ", 
  SqrtBox["15"], " ", 
  RowBox[{"Cos", "[", 
   RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]], "Output",
 CellChangeTimes->{3.472760669745635*^9, 3.473001343076909*^9, 
  3.571083261401033*^9}],

Cell[BoxData[
 RowBox[{"16", " ", 
  SqrtBox["15"], " ", "n", " ", "\[Pi]", " ", 
  RowBox[{"Sin", "[", 
   RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]], "Output",
 CellChangeTimes->{3.472760669745635*^9, 3.473001343076909*^9, 
  3.571083261413146*^9}],

Cell[BoxData[
 RowBox[{"16", " ", 
  SqrtBox["15"], " ", 
  SuperscriptBox["n", "2"], " ", 
  SuperscriptBox["\[Pi]", "2"], " ", 
  RowBox[{"Cos", "[", 
   RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]], "Output",
 CellChangeTimes->{3.472760669745635*^9, 3.473001343076909*^9, 
  3.571083261426723*^9}]
}, Open  ]],

Cell[TextData[{
 "The short of it: the ",
 Cell[BoxData[
  SuperscriptBox["n", 
   RowBox[{"-", "3"}]]],
  CellChangeTimes->{{3.4727607416421223`*^9, 3.4727607464456053`*^9}}],
 " factors that were responsible for the initially rapid convergence lose \
force with each differentiation, disappear altogether after 3 \
differentiations, and thereafter become \"divergence factors.\"  "
}], "Text",
 CellChangeTimes->{{3.47276071342245*^9, 3.472760812314733*^9}, {
  3.472760855954389*^9, 3.472760916573575*^9}}],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.472765518498515*^9, 3.4727655279305773`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Expected value of energysquared", "Subsection",
 CellChangeTimes->{{3.472310805194643*^9, 3.472310828946022*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpectedEnergySquared", "=", 
  RowBox[{
   SubsuperscriptBox["\[Integral]", "0", "1"], 
   RowBox[{
    RowBox[{"\[Psi]", "[", "x", "]"}], 
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["\[ScriptCapitalH]", "2"], " ", 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"x", ",", "4"}], "}"}]}], "]"}]}], ")"}], 
    RowBox[{"\[DifferentialD]", "x"}]}]}]}]], "Input",
 CellChangeTimes->{{3.472311155179411*^9, 3.472311178565134*^9}, {
  3.473001400548492*^9, 3.473001437758504*^9}}],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.472311186594759*^9, 3.472760995073104*^9, 
  3.472765323278335*^9, 3.473001385098751*^9, 3.473001441602899*^9, 
  3.571083261608671*^9}]
}, Open  ]],

Cell[TextData[{
 "That result is surprising, but understandable: ",
 StyleBox["\[Psi][x]", "Output"],
 " is a quadratic function of ",
 StyleBox["x", "Output"],
 ", so is killed by 4th order differentiation. \n\nIf, on the other hand, we \
proceed from the spectral representation of \[Psi] we already got "
}], "Text",
 CellChangeTimes->{{3.4723113346439667`*^9, 3.472311406788072*^9}, {
  3.472311513956668*^9, 3.47231154803205*^9}, {3.472311629681262*^9, 
  3.472311656094255*^9}, {3.472765563516873*^9, 3.4727655660011377`*^9}, {
  3.473001459979999*^9, 3.4730015062852077`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SpectrallyExpectedEnergy", "=", 
  RowBox[{"\[ScriptCapitalE]", 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "0"}], "\[Infinity]"], 
    RowBox[{
     SuperscriptBox[
      RowBox[{"c", "[", "k", "]"}], "2"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", "k"}], "+", "1"}], ")"}], "2"]}]}]}]}]], "Input",
 CellChangeTimes->{{3.472761129249647*^9, 3.4727611546714783`*^9}, {
  3.472761230534596*^9, 3.472761239609164*^9}, {3.472765336675527*^9, 
  3.472765338809811*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"5", " ", 
   SuperscriptBox["\[HBar]", "2"]}], "m"]], "Output",
 CellChangeTimes->{3.4727611612775087`*^9, 3.47276124473778*^9, 
  3.47276534777775*^9, 3.473001512577754*^9, 3.5710832617283497`*^9}]
}, Open  ]],

Cell["and now get", "Text",
 CellChangeTimes->{{3.4727655712631207`*^9, 3.472765572854841*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SpectrallyExpectedEnergySquared", "=", 
  RowBox[{
   SuperscriptBox["\[ScriptCapitalE]", "2"], 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "0"}], "\[Infinity]"], 
    RowBox[{
     SuperscriptBox[
      RowBox[{"c", "[", "k", "]"}], "2"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", "k"}], "+", "1"}], ")"}], "4"]}]}]}]}]], "Input",
 CellChangeTimes->{{3.472311231380999*^9, 3.472311244653948*^9}, 
   3.472761098409556*^9, {3.472761256610786*^9, 3.472761258268135*^9}, {
   3.472765361537519*^9, 3.472765367727462*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"30", " ", 
   SuperscriptBox["\[HBar]", "4"]}], 
  SuperscriptBox["m", "2"]]], "Output",
 CellChangeTimes->{3.472311250229785*^9, 3.472761106927308*^9, 
  3.4727612634012327`*^9, 3.472765372115613*^9, 3.4730015346513233`*^9, 
  3.571083261872005*^9}]
}, Open  ]],

Cell[TextData[{
 "which is ",
 StyleBox["non",
  FontWeight->"Bold"],
 "-zero. We have arrived at a ",
 StyleBox["contradiction", "Subsection",
  FontSize->16],
 ":"
}], "Text",
 CellChangeTimes->{{3.472765696670415*^9, 3.47276574341088*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpectedEnergySquared", "-", 
  "SpectrallyExpectedEnergySquared"}]], "Input",
 CellChangeTimes->{{3.4727655963618393`*^9, 3.4727656050411*^9}, 
   3.473001555152398*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"30", " ", 
    SuperscriptBox["\[HBar]", "4"]}], 
   SuperscriptBox["m", "2"]]}]], "Output",
 CellChangeTimes->{3.4727656103463917`*^9, 3.473001566778487*^9, 
  3.571083261984226*^9}]
}, Open  ]],

Cell["\<\
In third order (as in all higher orders) the results yielded by the two \
methods differ even more profoundly: the first method yields 0 in every case, \
while the second method leads in every case to series that (for the reason \
stated just above) diverge: we have\
\>", "Text",
 CellChangeTimes->{{3.4723117162982616`*^9, 3.4723119125824966`*^9}, 
   3.47231198877067*^9, {3.4723146064195337`*^9, 3.472314614367136*^9}, {
   3.472765752219575*^9, 3.47276575611874*^9}, {3.4727660869992237`*^9, 
   3.472766108335535*^9}, {3.4730020343574944`*^9, 3.473002035444511*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SpectrallyExpectedEnergyCubed", "=", 
  RowBox[{
   SuperscriptBox["\[ScriptCapitalE]", "3"], 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "0"}], "p"], 
    RowBox[{
     SuperscriptBox[
      RowBox[{"c", "[", "k", "]"}], "2"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", "k"}], "+", "1"}], ")"}], "6"]}]}]}]}]], "Input",
 CellChangeTimes->{{3.4727613211184893`*^9, 3.472761335996024*^9}, {
   3.472766116422933*^9, 3.472766118502315*^9}, {3.473001607964328*^9, 
   3.47300160813168*^9}, {3.473001641108323*^9, 3.4730016499565077`*^9}, {
   3.473001717244673*^9, 3.473001778353077*^9}, 3.4730019695114937`*^9, {
   3.473002022629129*^9, 3.473002027058898*^9}, 3.473002152628533*^9}],

Cell[BoxData[
 FractionBox[
  RowBox[{"120", " ", 
   RowBox[{"(", 
    RowBox[{"1", "+", "p"}], ")"}], " ", 
   SuperscriptBox["\[HBar]", "6"]}], 
  SuperscriptBox["m", "3"]]], "Output",
 CellChangeTimes->{3.473002156123811*^9, 3.571083262139902*^9}]
}, Open  ]],

Cell["\<\
which blows up in the limit p \[LongRightArrow] \[Infinity].\
\>", "Text",
 CellChangeTimes->{{3.473002046979844*^9, 3.47300205907517*^9}, {
  3.473002126978771*^9, 3.473002131090172*^9}}],

Cell["\<\
The evident source of the contradiction: we have arrived at a situation in \
which\
\>", "Text",
 CellChangeTimes->{{3.472766153849625*^9, 3.472766177025833*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"derivative", " ", "of", " ", "infinite", " ", "sum"}], " ", 
  "\[NotEqual]", 
  RowBox[{"infinite", " ", "sum", " ", "of", " ", "derivatives"}]}]], "Input",\

 CellChangeTimes->{{3.472766191093844*^9, 3.472766209290275*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"derivative", " ", "infinite", " ", "of", " ", "sum"}], 
  "\[NotEqual]", 
  RowBox[{"derivatives", " ", "infinite", " ", "of", " ", "sum"}]}]], "Output",\

 CellChangeTimes->{3.571083262244121*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.472766758231803*^9, 3.4727667608933563`*^9}}],

Cell[TextData[{
 StyleBox["REMARK",
  FontWeight->"Bold",
  FontColor->RGBColor[1, 0, 0]],
 ": It is clear already on dimensional grounds that relaxation of our \
assumption that the box width a = 1 entails"
}], "Text",
 CellChangeTimes->{{3.4727665562759542`*^9, 3.472766563417429*^9}, {
  3.472766619111047*^9, 3.472766738243526*^9}}],

Cell[BoxData[
 RowBox[{
  FractionBox[
   SuperscriptBox["\[HBar]", "2"], "m"], "\[Rule]", 
  FractionBox[
   SuperscriptBox["\[HBar]", "2"], 
   RowBox[{"m", " ", 
    SuperscriptBox["a", "2"]}]]}]], "Output",
 CellChangeTimes->{{3.472766766209145*^9, 3.472766807511764*^9}}],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.472314677871125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Variance", "Subsection",
 CellChangeTimes->{{3.4723146831692667`*^9, 3.472314694494088*^9}}],

Cell["By definition", "Text",
 CellChangeTimes->{{3.472314822640904*^9, 3.472314824978559*^9}}],

Cell[BoxData[
 RowBox[{"Variance", "=", 
  RowBox[{"ExpectedEnergySquared", "-", 
   SuperscriptBox[
    RowBox[{"(", "ExpectedEnergy", ")"}], "2"]}]}]], "Output",
 CellChangeTimes->{{3.472314840431169*^9, 3.4723148785280046`*^9}}],

Cell["The spectral method supplies", "Text",
 CellChangeTimes->{{3.472314787665339*^9, 3.4723147947756577`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SpectrallyExpectedEnergySquared", "-", 
  SuperscriptBox[
   RowBox[{"(", "SpectrallyExpectedEnergy", ")"}], "2"]}]], "Input",
 CellChangeTimes->{{3.472315027867585*^9, 3.472315051091989*^9}, {
  3.472766241274892*^9, 3.4727662738403177`*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"5", " ", 
   SuperscriptBox["\[HBar]", "4"]}], 
  SuperscriptBox["m", "2"]]], "Output",
 CellChangeTimes->{3.472315055735408*^9, 3.472766292819457*^9, 
  3.4730022059136143`*^9, 3.5710832628433104`*^9}]
}, Open  ]],

Cell["while direct calculation leads to the nonsensical result", "Text",
 CellChangeTimes->{{3.4723151127585773`*^9, 3.472315130904834*^9}, {
  3.472315165499288*^9, 3.472315177173518*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpectedEnergySquared", "-", 
  SuperscriptBox[
   RowBox[{"(", "ExpectedEnergy", ")"}], "2"]}]], "Input",
 CellChangeTimes->{{3.472315139343679*^9, 3.472315148391388*^9}, {
  3.472766350035005*^9, 3.472766359321672*^9}}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"25", " ", 
    SuperscriptBox["\[HBar]", "4"]}], 
   SuperscriptBox["m", "2"]]}]], "Output",
 CellChangeTimes->{3.472766363228491*^9, 3.4730022157812757`*^9, 
  3.571083262995344*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.472767954758247*^9, 3.472767954869925*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Dynamical manifestation of the same problem", "Subsection",
 CellChangeTimes->{{3.4728321193317547`*^9, 3.472832130028*^9}, {
  3.473002244427236*^9, 3.473002249415474*^9}}],

Cell["Working as before from", "Text",
 CellChangeTimes->{{3.473002343218346*^9, 3.473002346977418*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"H", "=", 
  RowBox[{
   RowBox[{"-", "\[ScriptCapitalH]"}], 
   RowBox[{
    SubscriptBox["\[PartialD]", 
     RowBox[{"x", ",", "x"}]], "\[Placeholder]"}]}]}]], "Input",
 CellChangeTimes->{3.473002384755829*^9}],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.5710832631767483`*^9}]
}, Open  ]],

Cell["we expect to have", "Text",
 CellChangeTimes->{{3.4730024168619967`*^9, 3.473002420189183*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptCapitalH]", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Phi]", "[", 
   RowBox[{"x", ",", "t"}], "]"}], "=", 
  RowBox[{
   UnderoverscriptBox["\[Sum]", 
    RowBox[{"k", "=", "0"}], "\[Infinity]"], 
   RowBox[{
    FractionBox["1", 
     RowBox[{"k", "!"}]], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", 
        FractionBox["\[ImaginaryI]", "\[HBar]"]}], "\[ScriptCapitalH]", " ", 
       "t"}], ")"}], "k"], 
    RowBox[{"D", "[", 
     RowBox[{
      RowBox[{"\[Phi]", "[", "x", "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"2", "k"}]}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalH]", "=", 
   FractionBox[
    SuperscriptBox["\[HBar]", "2"], 
    RowBox[{"2", "m"}]]}], ";"}]}], "Input",
 CellChangeTimes->{{3.473003365652169*^9, 3.4730033690791397`*^9}, {
  3.473003492698905*^9, 3.4730035031924477`*^9}}],

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  FractionBox[
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"-", 
       FractionBox[
        RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[ScriptCapitalH]"}], 
        "\[HBar]"]}], ")"}], "k"], " ", 
    RowBox[{
     SuperscriptBox["\[Phi]", 
      TagBox[
       RowBox[{"(", 
        RowBox[{"2", " ", "k"}], ")"}],
       Derivative],
      MultilineFunction->None], "[", "x", "]"}]}], 
   RowBox[{"k", "!"}]]}]], "Output",
 CellChangeTimes->{3.473003514306693*^9, 3.571083266649128*^9}]
}, Open  ]],

Cell["\<\
Looking to the motion of the individual energy eigenfunctions, we have\
\>", "Text",
 CellChangeTimes->{{3.47300261774008*^9, 3.473002642447482*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"k", ",", 
      FractionBox[
       RowBox[{"D", "[", 
        RowBox[{
         RowBox[{"e", "[", 
          RowBox[{"x", ",", "n"}], "]"}], ",", 
         RowBox[{"{", 
          RowBox[{"x", ",", 
           RowBox[{"2", "k"}]}], "}"}]}], "]"}], 
       RowBox[{"e", "[", 
        RowBox[{"x", ",", "n"}], "]"}]]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"k", ",", "0", ",", "4"}], "}"}]}], "]"}], "//", 
  "TableForm"}]], "Input",
 CellChangeTimes->{{3.472847821673327*^9, 3.472847921334919*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"0", "1"},
    {"1", 
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["n", "2"]}], " ", 
      SuperscriptBox["\[Pi]", "2"]}]},
    {"2", 
     RowBox[{
      SuperscriptBox["n", "4"], " ", 
      SuperscriptBox["\[Pi]", "4"]}]},
    {"3", 
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["n", "6"]}], " ", 
      SuperscriptBox["\[Pi]", "6"]}]},
    {"4", 
     RowBox[{
      SuperscriptBox["n", "8"], " ", 
      SuperscriptBox["\[Pi]", "8"]}]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.472847904999919*^9, 3.472847923127644*^9}, 
   3.47300265869987*^9, 3.57108326729281*^9}]
}, Open  ]],

Cell["whence", "Text",
 CellChangeTimes->{{3.473002683951988*^9, 3.473002687613575*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  RowBox[{
   FractionBox["1", 
    RowBox[{"k", "!"}]], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       FractionBox["\[ImaginaryI]", "\[HBar]"]}], "\[ScriptCapitalH]", " ", 
      "t"}], ")"}], "k"], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["n", "2"]}], " ", 
      SuperscriptBox["\[Pi]", "2"]}], ")"}], "k"], 
   RowBox[{"(", 
    RowBox[{"nth", ".", "eigenstate"}], ")"}]}]}]], "Input",
 CellChangeTimes->{
  3.473002734943057*^9, {3.473002948040572*^9, 3.473002986810618*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["n", "2"], " ", 
     SuperscriptBox["\[Pi]", "2"], " ", "t", " ", "\[HBar]"}], 
    RowBox[{"2", " ", "m"}]]], " ", 
  RowBox[{"nth", ".", "eigenstate"}]}]], "Output",
 CellChangeTimes->{
  3.473002746382189*^9, {3.473002960757895*^9, 3.4730029883733377`*^9}, 
   3.571083268010988*^9}]
}, Open  ]],

Cell["which\[LongDash]when we recall that", "Text",
 CellChangeTimes->{{3.473003014524025*^9, 3.4730030374397984`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[ScriptCapitalE]", " ", 
  SuperscriptBox["n", "2"]}]], "Input",
 CellChangeTimes->{{3.4730029172774477`*^9, 3.4730029190173407`*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SuperscriptBox["n", "2"], " ", 
   SuperscriptBox["\[Pi]", "2"], " ", 
   SuperscriptBox["\[HBar]", "2"]}], 
  RowBox[{"2", " ", "m"}]]], "Output",
 CellChangeTimes->{3.473002815663299*^9, 3.473002921175313*^9, 
  3.5710832683032093`*^9}]
}, Open  ]],

Cell[TextData[{
 "is just ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["\[ScriptCapitalE]", "n"], TraditionalForm]],
  FormatType->"TraditionalForm"],
 "\[LongDash]gives back the familiar fact that the energy eigenstates simply \
buzz:"
}], "Text",
 CellChangeTimes->{{3.473003083180849*^9, 3.4730031001320953`*^9}, {
  3.4730032125689173`*^9, 3.47300323564005*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SubscriptBox[
   RowBox[{"(", 
    RowBox[{"nth", ".", "eigenstate"}], ")"}], "t"], "=", 
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     FractionBox["\[ImaginaryI]", "\[HBar]"], 
     SubscriptBox["\[ScriptCapitalE]", "n"], "t"}]], 
   SubscriptBox[
    RowBox[{"(", 
     RowBox[{"nth", ".", "eigenstate"}], ")"}], "0"]}]}]], "Input",
 CellChangeTimes->{{3.473003123757711*^9, 3.473003188918538*^9}, {
  3.4730032824677763`*^9, 3.473003286141676*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", "t", " ", 
     SubscriptBox[
      RowBox[{"(", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[Pi]", "2"], " ", 
         SuperscriptBox["\[HBar]", "2"]}], 
        RowBox[{"2", " ", "m"}]], ")"}], "n"]}], "\[HBar]"]], " ", 
  SubscriptBox[
   RowBox[{"(", 
    RowBox[{"nth", ".", "eigenstate"}], ")"}], "0"]}]], "Output",
 CellChangeTimes->{3.571083268469593*^9}]
}, Open  ]],

Cell["Here I automate the demonstration:", "Text",
 CellChangeTimes->{{3.473004140935461*^9, 3.473004150940724*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{"\[ScriptCapitalH]", ",", "\[ScriptCapitalE]"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  RowBox[{
   FractionBox["1", 
    RowBox[{"k", "!"}]], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], " ", "\[ScriptCapitalH]", " ", "t"}], 
     ")"}], "k"], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"e", "[", 
      RowBox[{"x", ",", "n"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"2", "k"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "/.", 
   RowBox[{
    RowBox[{
     SubscriptBox["\[PartialD]", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"2", " ", "k"}]}], "}"}]], 
     RowBox[{"(", 
      RowBox[{
       SqrtBox["2"], " ", 
       RowBox[{"Sin", "[", 
        RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}], ")"}]}], "\[Rule]", 
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", 
         SuperscriptBox["n", "2"]}], " ", 
        SuperscriptBox["\[Pi]", "2"]}], ")"}], "k"], 
     SqrtBox["2"], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"%", "/.", 
  RowBox[{
   RowBox[{"\[ImaginaryI]", " ", 
    SuperscriptBox["n", "2"], " ", 
    SuperscriptBox["\[Pi]", "2"], " ", "t", " ", "\[ScriptCapitalH]"}], 
   "\[Rule]", 
   RowBox[{
    FractionBox["\[ImaginaryI]", "\[HBar]"], 
    SubscriptBox["\[ScriptCapitalE]", "n"], 
    "t"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalH]", "=", 
   FractionBox[
    SuperscriptBox["\[HBar]", "2"], 
    RowBox[{"2", "m"}]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]", "=", 
   RowBox[{
    SuperscriptBox["n", "2"], " ", 
    SuperscriptBox["\[Pi]", "2"], " ", "\[ScriptCapitalH]"}]}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.472870242254015*^9, 3.472870287781272*^9}, {
   3.472870654997881*^9, 3.4728706566545277`*^9}, {3.473003592096657*^9, 
   3.473003602716736*^9}, {3.473003636430431*^9, 3.473003664460745*^9}, {
   3.473003739779133*^9, 3.473003740274584*^9}, 3.473003855342969*^9, {
   3.473003953139708*^9, 3.473004005935933*^9}, {3.473004050688621*^9, 
   3.4730040894422493`*^9}}],

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  FractionBox[
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[ScriptCapitalH]"}], 
      ")"}], "k"], " ", 
    RowBox[{
     SubscriptBox["\[PartialD]", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"2", " ", "k"}]}], "}"}]], 
     RowBox[{"(", 
      RowBox[{
       SqrtBox["2"], " ", 
       RowBox[{"Sin", "[", 
        RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}], ")"}]}]}], 
   RowBox[{"k", "!"}]]}]], "Output",
 CellChangeTimes->{
  3.47287033009304*^9, 3.472870475540085*^9, 3.4728706659103947`*^9, 
   3.473003623407321*^9, {3.4730036555058117`*^9, 3.473003665659625*^9}, 
   3.473003748819394*^9, 3.473003866397106*^9, 3.4730039098660307`*^9, 
   3.4730040962159557`*^9, 3.571083268918769*^9}],

Cell[BoxData[
 RowBox[{
  SqrtBox["2"], " ", 
  SuperscriptBox["\[ExponentialE]", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", "t", " ", 
     SubscriptBox["\[ScriptCapitalE]", "n"]}], "\[HBar]"]], " ", 
  RowBox[{"Sin", "[", 
   RowBox[{"n", " ", "\[Pi]", " ", "x"}], "]"}]}]], "Output",
 CellChangeTimes->{
  3.47287033009304*^9, 3.472870475540085*^9, 3.4728706659103947`*^9, 
   3.473003623407321*^9, {3.4730036555058117`*^9, 3.473003665659625*^9}, 
   3.473003748819394*^9, 3.473003866397106*^9, 3.4730039098660307`*^9, 
   3.4730040962159557`*^9, 3.571083269792203*^9}]
}, Open  ]],

Cell["\<\
Given the spectral representation of a state, we have only to launch each of \
its components into motion to set the whole state into motion. Which we now \
demonstrate as it pertains to the parabolic test state. Define\
\>", "Text",
 CellChangeTimes->{{3.473005443817767*^9, 3.473005536368189*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"e", "[", 
   RowBox[{"x_", ",", "n_", ",", "t_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "n"}], "]"}], 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], " ", 
     SuperscriptBox["n", "2"], "t"}]]}]}]], "Input"],

Cell["\<\
where as a matter of computational convenience I have set \[ScriptCapitalE]/\
\[HBar] = 1. Construct the truncated spectral series (I want only provide \
proof of method, though we know that inclusion of higher-order terms would \
have little quantitative effect)\
\>", "Text",
 CellChangeTimes->{{3.473005591600751*^9, 3.473005631250567*^9}, {
  3.473005770901843*^9, 3.473005774873808*^9}, {3.473005814971037*^9, 
  3.473005830070519*^9}, {3.473008120462804*^9, 3.473008172441126*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[CapitalPsi]", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{
   UnderoverscriptBox["\[Sum]", 
    RowBox[{"k", "=", "0"}], "2"], 
   RowBox[{
    RowBox[{"c", "[", "k", "]"}], 
    RowBox[{"e", "[", 
     RowBox[{"x", ",", 
      RowBox[{
       RowBox[{"2", "k"}], "+", "1"}], ",", "t"}], "]"}]}]}]}]], "Input"],

Cell["and use", "Text",
 CellChangeTimes->{{3.473005847205235*^9, 3.473005848269211*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   StyleBox["CompConj",
    FontColor->GrayLevel[0]], "[", "A_", "]"}], " ", ":=", " ", 
  RowBox[{"A", " ", "/.", "\[InvisibleSpace]", 
   RowBox[{
    RowBox[{"Complex", "[", 
     RowBox[{"0", ",", "n_"}], "]"}], "->", 
    RowBox[{"-", 
     RowBox[{"Complex", "[", 
      RowBox[{"0", ",", "n"}], "]"}]}]}]}]}]], "Input"],

Cell["to construct", "Text",
 CellChangeTimes->{{3.473005928993157*^9, 3.4730059308964157`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Conj\[CapitalPsi]", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{"CompConj", "[", 
   RowBox[{"\[CapitalPsi]", "[", 
    RowBox[{"x", ",", "t"}], "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.473005878937874*^9, 3.473005936980332*^9}}],

Cell["Those functions look like this", "Text",
 CellChangeTimes->{{3.4730081955913353`*^9, 3.473008210926667*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"\[CapitalPsi]", "[", 
  RowBox[{"x", ",", "t"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Conj\[CapitalPsi]", "[", 
  RowBox[{"x", ",", "t"}], "]"}]}], "Input",
 CellChangeTimes->{{3.473005961125002*^9, 3.473005988895924*^9}}],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox["30"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}]}], 
   SuperscriptBox["\[Pi]", "3"]], "+", 
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox[
     FractionBox["10", "3"]], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "9"}], " ", "\[ImaginaryI]", " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"9", " ", 
    SuperscriptBox["\[Pi]", "3"]}]], "+", 
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox[
     FractionBox["6", "5"]], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "25"}], " ", "\[ImaginaryI]", " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"25", " ", 
    SuperscriptBox["\[Pi]", "3"]}]]}]], "Output",
 CellChangeTimes->{{3.473005973919314*^9, 3.473005990756776*^9}, 
   3.571083270454446*^9}],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox["30"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"\[ImaginaryI]", " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}]}], 
   SuperscriptBox["\[Pi]", "3"]], "+", 
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox[
     FractionBox["10", "3"]], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"9", " ", "\[ImaginaryI]", " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"9", " ", 
    SuperscriptBox["\[Pi]", "3"]}]], "+", 
  FractionBox[
   RowBox[{"8", " ", 
    SqrtBox[
     FractionBox["6", "5"]], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"25", " ", "\[ImaginaryI]", " ", "t"}]], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"25", " ", 
    SuperscriptBox["\[Pi]", "3"]}]]}]], "Output",
 CellChangeTimes->{{3.473005973919314*^9, 3.473005990756776*^9}, 
   3.571083270521953*^9}]
}, Open  ]],

Cell["\<\
and become rapidly more unwieldly as one moves to higher order. Construct\
\>", "Text",
 CellChangeTimes->{{3.473006045522214*^9, 3.473006052417242*^9}, {
  3.4730082241417*^9, 3.473008253900004*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"MovingProbDensity", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{"ComplexExpand", "[", 
   RowBox[{
    RowBox[{"\[CapitalPsi]", "[", 
     RowBox[{"x", ",", "t"}], "]"}], 
    RowBox[{"CompConj", "[", 
     RowBox[{"\[CapitalPsi]", "[", 
      RowBox[{"x", ",", "t"}], "]"}], "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4727684349334908`*^9, 3.47276845340022*^9}, {
  3.472768511462473*^9, 3.472768519349347*^9}, {3.472768637228548*^9, 
  3.472768658422861*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MovingProbDensity", "[", 
  RowBox[{"x", ",", "t"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"1920", " ", 
    SuperscriptBox[
     RowBox[{"Cos", "[", "t", "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"\[Pi]", " ", "x"}], "]"}], "2"]}], 
   SuperscriptBox["\[Pi]", "6"]], "+", 
  FractionBox[
   RowBox[{"1920", " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", "t", "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"\[Pi]", " ", "x"}], "]"}], "2"]}], 
   SuperscriptBox["\[Pi]", "6"]], "+", 
  FractionBox[
   RowBox[{"1280", " ", 
    RowBox[{"Cos", "[", "t", "]"}], " ", 
    RowBox[{"Cos", "[", 
     RowBox[{"9", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"9", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"1280", " ", 
    RowBox[{"Sin", "[", "t", "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"9", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"9", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"640", " ", 
    SuperscriptBox[
     RowBox[{"Cos", "[", 
      RowBox[{"9", " ", "t"}], "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}], "2"]}], 
   RowBox[{"243", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"640", " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"9", " ", "t"}], "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}], "2"]}], 
   RowBox[{"243", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"768", " ", 
    RowBox[{"Cos", "[", "t", "]"}], " ", 
    RowBox[{"Cos", "[", 
     RowBox[{"25", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"25", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"768", " ", 
    RowBox[{"Sin", "[", "t", "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"25", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"25", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"256", " ", 
    RowBox[{"Cos", "[", 
     RowBox[{"9", " ", "t"}], "]"}], " ", 
    RowBox[{"Cos", "[", 
     RowBox[{"25", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"225", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"256", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"9", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"25", " ", "t"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}], " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"225", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"384", " ", 
    SuperscriptBox[
     RowBox[{"Cos", "[", 
      RowBox[{"25", " ", "t"}], "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}], "2"]}], 
   RowBox[{"3125", " ", 
    SuperscriptBox["\[Pi]", "6"]}]], "+", 
  FractionBox[
   RowBox[{"384", " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"25", " ", "t"}], "]"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", 
      RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}], "2"]}], 
   RowBox[{"3125", " ", 
    SuperscriptBox["\[Pi]", "6"]}]]}]], "Output",
 CellChangeTimes->{3.473006210139206*^9, 3.473007498695635*^9, 
  3.4730075711109247`*^9, 3.571083270942*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TrigReduce", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.473007508279908*^9, 3.473007513715179*^9}}],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{
   FractionBox["1", 
    RowBox[{"759375", " ", 
     SuperscriptBox["\[Pi]", "6"]}]], 
   RowBox[{"64", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "11406979"}], "+", 
      RowBox[{"11390625", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
      RowBox[{"15625", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{"6", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
      RowBox[{"729", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{"10", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
      RowBox[{"3375", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"16", " ", "t"}], "-", 
         RowBox[{"8", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
      RowBox[{"91125", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"24", " ", "t"}], "-", 
         RowBox[{"6", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
      RowBox[{"421875", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"8", " ", "t"}], "-", 
         RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"91125", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"24", " ", "t"}], "-", 
         RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"421875", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"8", " ", "t"}], "-", 
         RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"3375", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"16", " ", "t"}], "-", 
         RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"421875", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"8", " ", "t"}], "+", 
         RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"3375", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"16", " ", "t"}], "+", 
         RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
      RowBox[{"421875", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"8", " ", "t"}], "+", 
         RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
      RowBox[{"91125", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"24", " ", "t"}], "+", 
         RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
      RowBox[{"91125", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"24", " ", "t"}], "+", 
         RowBox[{"6", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
      RowBox[{"3375", " ", 
       RowBox[{"Cos", "[", 
        RowBox[{
         RowBox[{"16", " ", "t"}], "+", 
         RowBox[{"8", " ", "\[Pi]", " ", "x"}]}], "]"}]}]}], 
     ")"}]}]}]}]], "Output",
 CellChangeTimes->{3.4730075158636713`*^9, 3.473007575073123*^9, 
  3.571083271363058*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"ReducedMovingProbDensity", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"759375", " ", 
      SuperscriptBox["\[Pi]", "6"]}]]}], "64", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "11406979"}], "+", 
     RowBox[{"11390625", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{"2", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
     RowBox[{"15625", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{"6", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
     RowBox[{"729", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{"10", " ", "\[Pi]", " ", "x"}], "]"}]}], "+", 
     RowBox[{"3375", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"16", " ", "t"}], "-", 
        RowBox[{"8", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
     RowBox[{"91125", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"24", " ", "t"}], "-", 
        RowBox[{"6", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
     RowBox[{"421875", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"8", " ", "t"}], "-", 
        RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"91125", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"24", " ", "t"}], "-", 
        RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"421875", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"8", " ", "t"}], "-", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"3375", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"16", " ", "t"}], "-", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"421875", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"8", " ", "t"}], "+", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"3375", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"16", " ", "t"}], "+", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
     RowBox[{"421875", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"8", " ", "t"}], "+", 
        RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "-", 
     RowBox[{"91125", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"24", " ", "t"}], "+", 
        RowBox[{"4", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
     RowBox[{"91125", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"24", " ", "t"}], "+", 
        RowBox[{"6", " ", "\[Pi]", " ", "x"}]}], "]"}]}], "+", 
     RowBox[{"3375", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{
        RowBox[{"16", " ", "t"}], "+", 
        RowBox[{"8", " ", "\[Pi]", " ", "x"}]}], "]"}]}]}], 
    ")"}]}]}]], "Input",
 CellChangeTimes->{{3.472769058614216*^9, 3.472769093117826*^9}, {
   3.4727698140870743`*^9, 3.4727698160340967`*^9}, {3.4727897149933643`*^9, 
   3.472789726850842*^9}, {3.4730062293024063`*^9, 3.473006243833208*^9}, {
   3.473007531375741*^9, 3.473007537742715*^9}, 3.473007593530479*^9}],

Cell["\<\
Note that the first cycle of this periodic function is complete at time t = 2\
\[Pi]/8.\
\>", "Text",
 CellChangeTimes->{{3.473007987878518*^9, 3.473008030129106*^9}}],

Cell["\<\
I construct now a figure illustrating how the moving density compares with \
its initial structure\
\>", "Text",
 CellChangeTimes->{{3.473007895265881*^9, 3.47300792069598*^9}, {
  3.473008042185276*^9, 3.473008050000472*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 SuperscriptBox[
  RowBox[{"\[Psi]", "[", "x", "]"}], "2"]], "Input",
 CellChangeTimes->{{3.47300792620325*^9, 3.473007929185463*^9}}],

Cell[BoxData[
 RowBox[{"30", " ", 
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{"1", "-", "x"}], ")"}], "2"], " ", 
  SuperscriptBox["x", "2"]}]], "Output",
 CellChangeTimes->{3.473006528965972*^9, 3.473007930378005*^9, 
  3.571083271540732*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"\[Psi]", "[", "x", "]"}], "2"], ",", 
       RowBox[{"Evaluate", "[", 
        RowBox[{"ReducedMovingProbDensity", "[", 
         RowBox[{"x", ",", "t"}], "]"}], "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "2.5"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"t", ",", "0", ",", 
     FractionBox[
      RowBox[{"2", "\[Pi]"}], "8"]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.472790410082799*^9, 3.4727904336230288`*^9}, {
   3.473006295461814*^9, 3.4730063436230297`*^9}, {3.473006458035624*^9, 
   3.473006458407731*^9}, {3.473006494283643*^9, 3.473006497205249*^9}, {
   3.473006549718936*^9, 3.4730065557153807`*^9}, 3.473006626368246*^9, {
   3.4730066820924063`*^9, 3.473006682640602*^9}, {3.473006728338076*^9, 
   3.47300672877737*^9}, {3.473006764841516*^9, 3.473006771247109*^9}, {
   3.4730068092159863`*^9, 3.47300681355169*^9}, 3.473006916142819*^9, 
   3.473007338964773*^9, {3.473007416594919*^9, 3.4730074183626747`*^9}, {
   3.473007707231182*^9, 3.473007736019125*^9}, {3.4730077844500732`*^9, 
   3.473007809203876*^9}}],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`t$$ = 0.24033183799961916`, Typeset`show$$ =
     True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`t$$], 0, Rational[1, 4] Pi}}, Typeset`size$$ = {
    540., {171., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`t$10260$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, "Variables" :> {$CellContext`t$$ = 0}, 
      "ControllerVariables" :> {
        Hold[$CellContext`t$$, $CellContext`t$10260$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> 
      Plot[{$CellContext`\[Psi][$CellContext`x]^2, 
         Evaluate[
          $CellContext`ReducedMovingProbDensity[$CellContext`x, \
$CellContext`t$$]]}, {$CellContext`x, 0, 1}, PlotRange -> {0, 2.5}], 
      "Specifications" :> {{$CellContext`t$$, 0, Rational[1, 4] Pi}}, 
      "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{602., {236.03125, 243.96875}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{{3.472790443716578*^9, 3.472790458098007*^9}, {
   3.472824395057629*^9, 3.4728244060345163`*^9}, {3.473006141262488*^9, 
   3.473006164500578*^9}, 3.473006301892008*^9, {3.473006346215537*^9, 
   3.473006372781913*^9}, {3.473006460048607*^9, 3.4730064723778963`*^9}, {
   3.473006502387167*^9, 3.473006512560096*^9}, {3.473006561914213*^9, 
   3.4730065728093557`*^9}, {3.473006685903088*^9, 3.473006695278411*^9}, {
   3.4730067305282097`*^9, 3.473006738618389*^9}, {3.473006777259857*^9, 
   3.473006790898*^9}, {3.4730069183421173`*^9, 3.473006924945438*^9}, {
   3.47300734593517*^9, 3.473007361974825*^9}, {3.4730074209564333`*^9, 
   3.473007426901765*^9}, {3.473007713588572*^9, 3.4730077625470533`*^9}, {
   3.473007801171987*^9, 3.473007829830051*^9}, {3.473007947425022*^9, 
   3.473007954420967*^9}, {3.473008077215469*^9, 3.473008090122912*^9}, {
   3.473008288384571*^9, 3.473008300675848*^9}, {3.57108291217443*^9, 
   3.57108291541465*^9}, 3.571083271767466*^9}]
}, Open  ]],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.4730128325929203`*^9}],

Cell["\<\
We now abandon the spectral representation, and work directly from \
\>", "Text",
 CellChangeTimes->{{3.47301285566914*^9, 3.4730128719399633`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[Psi]", "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.47301287849452*^9, 3.473012882790222*^9}}],

Cell[BoxData[
 RowBox[{
  SqrtBox["30"], " ", 
  RowBox[{"(", 
   RowBox[{"1", "-", "x"}], ")"}], " ", "x"}]], "Output",
 CellChangeTimes->{3.473012883591851*^9, 3.571083272967865*^9}]
}, Open  ]],

Cell["We then find", "Text",
 CellChangeTimes->{{3.473013732938682*^9, 3.4730137346637917`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptCapitalH]", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  RowBox[{
   FractionBox["1", 
    RowBox[{"k", "!"}]], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], " ", "\[ScriptCapitalH]", " ", "t"}], 
     ")"}], "k"], 
   RowBox[{"D", "[", 
    RowBox[{
     RowBox[{"\[Psi]", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"2", "k"}]}], "}"}]}], "]"}]}]}]}], "Input",
 CellChangeTimes->{{3.473012943098716*^9, 3.473012989504586*^9}}],

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "\[Infinity]"], 
  FractionBox[
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[ScriptCapitalH]"}], 
      ")"}], "k"], " ", 
    RowBox[{
     SubscriptBox["\[PartialD]", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"2", " ", "k"}]}], "}"}]], 
     RowBox[{"(", 
      RowBox[{
       SqrtBox["30"], " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], ")"}]}]}], 
   RowBox[{"k", "!"}]]}]], "Output",
 CellChangeTimes->{{3.473012962876156*^9, 3.473012991495615*^9}, 
   3.571083273387022*^9}]
}, Open  ]],

Cell["which by", "Text",
 CellChangeTimes->{{3.473013766984864*^9, 3.473013768517624*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Table", "[", 
  RowBox[{
   RowBox[{
    SubscriptBox["\[PartialD]", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"2", " ", "k"}]}], "}"}]], 
    RowBox[{"(", 
     RowBox[{
      SqrtBox["30"], " ", 
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4730130255133953`*^9, 3.473013052678474*^9}, {
  3.473013756173573*^9, 3.473013756324279*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    SqrtBox["30"], " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], ",", 
   RowBox[{
    RowBox[{"-", "2"}], " ", 
    SqrtBox["30"]}], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", 
   "0", ",", "0", ",", "0", ",", "0"}], "}"}]], "Output",
 CellChangeTimes->{3.473013058908998*^9, 3.473013757367976*^9, 
  3.5710832735328703`*^9}]
}, Open  ]],

Cell["gives", "Text",
 CellChangeTimes->{{3.473013788228504*^9, 3.4730137893245277`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "0"}], "10"], 
  FractionBox[
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[ScriptCapitalH]"}], 
      ")"}], "k"], " ", 
    RowBox[{
     SubscriptBox["\[PartialD]", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"2", " ", "k"}]}], "}"}]], 
     RowBox[{"(", 
      RowBox[{
       SqrtBox["30"], " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], ")"}]}]}], 
   RowBox[{"k", "!"}]]}]], "Input",
 CellChangeTimes->{{3.4730133556084957`*^9, 3.473013374383917*^9}, {
  3.473013777477522*^9, 3.473013777651697*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SqrtBox["30"], " ", 
   RowBox[{"(", 
    RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], "+", 
  RowBox[{"2", " ", "\[ImaginaryI]", " ", 
   SqrtBox["30"], " ", "t", " ", "\[ScriptCapitalH]"}]}]], "Output",
 CellChangeTimes->{{3.473013357980451*^9, 3.473013375206352*^9}, 
   3.4730137975981817`*^9, 3.571083273870376*^9}]
}, Open  ]],

Cell["So we have ", "Text",
 CellChangeTimes->{{3.473013810919345*^9, 3.473013812946946*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"\[Psi]", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    SqrtBox["30"], " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], "+", 
   RowBox[{"2", " ", "\[ImaginaryI]", " ", 
    SqrtBox["30"], " ", "t", " ", 
    "\[ScriptCapitalH]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Conj\[Psi]", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{"CompConj", "[", 
   RowBox[{"\[Psi]", "[", 
    RowBox[{"x", ",", "t"}], "]"}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.47301331132967*^9, 3.473013325451394*^9}, {
  3.4730133853451147`*^9, 3.473013456735024*^9}}],

Cell["giving", "Text",
 CellChangeTimes->{{3.473013836913608*^9, 3.473013838001693*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"MMovingProbDensity", "[", 
   RowBox[{"x_", ",", "t_"}], "]"}], ":=", 
  RowBox[{"ComplexExpand", "[", 
   RowBox[{
    RowBox[{"\[Psi]", "[", 
     RowBox[{"x", ",", "t"}], "]"}], 
    RowBox[{"CompConj", "[", 
     RowBox[{"\[Psi]", "[", 
      RowBox[{"x", ",", "t"}], "]"}], "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4730135320682364`*^9, 3.473013545998931*^9}, {
  3.4730135926644163`*^9, 3.473013640402502*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MMovingProbDensity", "[", 
  RowBox[{"x", ",", "t"}], "]"}]], "Input",
 CellChangeTimes->{{3.4730136176531687`*^9, 3.473013619977911*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"30", " ", 
   SuperscriptBox["x", "2"]}], "-", 
  RowBox[{"60", " ", 
   SuperscriptBox["x", "3"]}], "+", 
  RowBox[{"30", " ", 
   SuperscriptBox["x", "4"]}], "+", 
  RowBox[{"120", " ", 
   SuperscriptBox["t", "2"], " ", 
   SuperscriptBox["\[ScriptCapitalH]", "2"]}]}]], "Output",
 CellChangeTimes->{{3.473013621436407*^9, 3.47301365062351*^9}, 
   3.571083274172264*^9}]
}, Open  ]],

Cell[TextData[{
 "The motion of ",
 StyleBox["\[Psi][x, t]", "Output"],
 " is clearly ",
 StyleBox["not periodic, nor is it even unitary",
  FontWeight->"Bold"],
 ":"
}], "Text",
 CellChangeTimes->{{3.473013862880192*^9, 3.473013923556549*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SubsuperscriptBox["\[Integral]", "0", "1"], 
  RowBox[{"%", 
   RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input",
 CellChangeTimes->{{3.4730136878884363`*^9, 3.473013700936027*^9}}],

Cell[BoxData[
 RowBox[{"1", "+", 
  RowBox[{"120", " ", 
   SuperscriptBox["t", "2"], " ", 
   SuperscriptBox["\[ScriptCapitalH]", "2"]}]}]], "Output",
 CellChangeTimes->{3.473013702475313*^9, 3.571083274506514*^9}]
}, Open  ]],

Cell[TextData[{
 "Our Hamiltonian has revcaled itself to be ",
 StyleBox["non-Hermitian",
  FontWeight->"Bold"],
 "."
}], "Text",
 CellChangeTimes->{{3.473013959740284*^9, 3.473013994024534*^9}}],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{3.5710907567024727`*^9}],

Cell[TextData[{
 StyleBox["MEMORANDA", "Subsection"],
 "\n"
}], "Text",
 CellChangeTimes->{{3.571090774364999*^9, 3.571090812756093*^9}}],

Cell["\<\
I had stewed about this problem for a couple of days when, on January 7th, I \
brought the problem to the attention of David Griffiths, who promptly \
responded as follows:\
\>", "Text",
 CellChangeTimes->{{3.4723191863449173`*^9, 3.472319220032589*^9}, {
  3.472319357890669*^9, 3.472319359142972*^9}, {3.571090941102159*^9, 
  3.571090991393228*^9}}],

Cell["\<\
Nick,

Here's my first guess as to your error: H^2 is not a valid operator (or \
rather, your second wave function is not in the space of functions for which \
it is well-defined/Hermitian).  Both your wave functions have kinks at each \
end, which means that the first derivative is discontinuous and the second \
carries a delta function.  You get away with ignoring this when you calculate \
<H> for the \"accidental\" reason reason that it is multiplied by a function \
that is zero at the ends, so the delta function does not contribute.  But \
when you go to H^2 you need two more derivatives (hence the second derivative \
of the delta function).  Integration by parts transfers them over to the \
other function, which means you now have the product of two deltas.  For some \
reason that works in the case of the ground state, but not in the case of the \
the quadratic.

Is this even vaguely relevant to your problem?

David\
\>", "Text",
 CellChangeTimes->{3.472319224109828*^9},
 FontColor->RGBColor[0, 0, 1]],

Cell["\<\
When (on January 11th\[LongDash]yesterday) I mentioned the problem with \
Darrell Schroeter he made an essentially similar remark: he suggested that my \
wave function might better be written\
\>", "Text",
 CellChangeTimes->{{3.472319297786707*^9, 3.472319383200652*^9}, {
   3.472319414171632*^9, 3.47231944751904*^9}, 3.472327826798554*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[CapitalPsi]", "[", 
   RowBox[{"x", ",", "a"}], "]"}], "=", 
  RowBox[{
   RowBox[{"\[Psi]", "[", 
    RowBox[{"x", ",", "a"}], "]"}], 
   RowBox[{"S", "[", 
    RowBox[{"x", ",", "a"}], "]"}]}]}]], "Output",
 CellChangeTimes->{{3.4723194629959507`*^9, 3.472319533304762*^9}}],

Cell[TextData[{
 "where ",
 StyleBox["S[x, a]", "Output"],
 " has unit value inside the box and vanishes outside the box. Those \
remarks/suggestions have motivated the preceeding discussion. \n\nI end with \
record of some commands that figured in earlier versions of this notebook, \
which I preserve for whatever they may someday prove to be worth:"
}], "Text",
 CellChangeTimes->{{3.472319810337818*^9, 3.472319870976997*^9}, {
  3.472328007549898*^9, 3.472328056233128*^9}, {3.571091017805304*^9, 
  3.5710910597706747`*^9}, {3.571091391402347*^9, 3.571091428646913*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"CoeffList", "=", 
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{
     SubsuperscriptBox["\[Integral]", "0", "1"], 
     RowBox[{"x", " ", 
      RowBox[{"e", "[", 
       RowBox[{"x", ",", "n"}], "]"}], 
      RowBox[{"\[DifferentialD]", "x"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "1", ",", "20"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4730926432585087`*^9, 3.473092666565897*^9}, {
  3.473092796395226*^9, 3.47309279659888*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   FractionBox[
    SqrtBox["2"], "\[Pi]"], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"3", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"2", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"5", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"3", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"7", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"4", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"9", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"5", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"11", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"6", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"13", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"7", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"15", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"8", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"17", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"9", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}], ",", 
   FractionBox[
    SqrtBox["2"], 
    RowBox[{"19", " ", "\[Pi]"}]], ",", 
   RowBox[{"-", 
    FractionBox["1", 
     RowBox[{"10", " ", 
      SqrtBox["2"], " ", "\[Pi]"}]]}]}], "}"}]], "Output",
 CellChangeTimes->{3.571091648840946*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"k", "=", "1"}], "20"], 
  RowBox[{
   RowBox[{
   "CoeffList", "\[LeftDoubleBracket]", "k", "\[RightDoubleBracket]"}], 
   RowBox[{"e", "[", 
    RowBox[{"x", ",", "k"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.473092702318718*^9, 3.473092743073682*^9}, {
  3.473092814823215*^9, 3.473092814996241*^9}}],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"\[Pi]", " ", "x"}], "]"}]}], "\[Pi]"], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"2", " ", "\[Pi]", " ", "x"}], "]"}], "\[Pi]"], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"3", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"4", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"2", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"5", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"6", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"3", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"7", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"7", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"8", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"4", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"9", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"9", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"10", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"5", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"11", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"11", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"12", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"6", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"13", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"13", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"14", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"7", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"15", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"15", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"16", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"8", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"17", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"17", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"18", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"9", " ", "\[Pi]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"Sin", "[", 
     RowBox[{"19", " ", "\[Pi]", " ", "x"}], "]"}]}], 
   RowBox[{"19", " ", "\[Pi]"}]], "-", 
  FractionBox[
   RowBox[{"Sin", "[", 
    RowBox[{"20", " ", "\[Pi]", " ", "x"}], "]"}], 
   RowBox[{"10", " ", "\[Pi]"}]]}]], "Output",
 CellChangeTimes->{3.571091691159699*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"\[Pi]", " ", "x"}], "]"}]}], "\[Pi]"], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"2", " ", "\[Pi]", " ", "x"}], "]"}], "\[Pi]"], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"3", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"3", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"4", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"2", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"5", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"5", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"6", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"3", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"7", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"7", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"8", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"4", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"9", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"9", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"10", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"5", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"11", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"11", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"12", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"6", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"13", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"13", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"14", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"7", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"15", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"15", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"16", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"8", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"17", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"17", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"18", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"9", " ", "\[Pi]"}]], "+", 
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{"Sin", "[", 
         RowBox[{"19", " ", "\[Pi]", " ", "x"}], "]"}]}], 
       RowBox[{"19", " ", "\[Pi]"}]], "-", 
      FractionBox[
       RowBox[{"Sin", "[", 
        RowBox[{"20", " ", "\[Pi]", " ", "x"}], "]"}], 
       RowBox[{"10", " ", "\[Pi]"}]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4730924886562157`*^9, 3.473092512349107*^9}, 
   3.4730927745868*^9, {3.473092833341113*^9, 3.473092871055818*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxFxW0w03EcAPCNdZRrjMr9adxE5SlOUlKpuMhDneHk8nRCWk/InXR1WrdJ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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwUl3k8lF8bxkmLUkgkoqKopKiU+MWlaLWkEFEqRIulJKTFUlkiJIkiIioR
yTJ2so2dsc1YZsYMklSUyJb3vP3T52ue55z7XNd132fmhJOVzAUeHp55PDwL
3f//v6bJ15LmwQtH/8uP5Pn/P6hIsK5Kas/XNLELu7CSsI7Ep+jI2J2aD2wz
H93T4oGBvJv3Bqk+zXjBZX3T63hgLBGT0VGvq5l1YeP+LvL5qbVzidJBGzTL
ubU8P0R5YCl//pn10RlNmsBN47MDPDgfcb689f6QZndiMq/DMA9sJMIKJ2xM
NfvPfmFEveaBbXRZjqR2ueYPe5cPFYd5cGntWLrGemXNsa6+BdUsHlxJkHt3
bl605nSJR+xjFR44yp+M9+HwYx5v5oKV5l64alxWT2PnYWHv5GthBx5cizh9
1MbwKpaGvkylXeaBc8dY5Z8SeSwPDgnc3+IFF4lH2n5KPRDTvXrGcAMPbljI
layKDYeEb+S3LTxecI0u2pssdBRrDiUUp0/ywI15Mvc/Tx7I1ArxG01q4eba
n7vqfmRjQ0GZp+RECTzO+2VYWtpj48ybSyxvL9xKWLftZ4MstgRfkVtD6r3d
R3nvrUGH0o3sAaHeEtyVP75JJDUY27vEtmVBC552X1+/lj4Alc0ftt6xWAcv
41Lh55V3sfutg5pQUhy8/jwy4N49BbVTosee5WnBO+LUI8XdKtircc51yMML
PqpytS4/hADTxaHbowl3/FpcmDiEfUa9K5dOn8N9iYe+x8TioDPlr+fIJJx3
svxZ/S0cnHLLY5eU4IHF+nnsBydxREK1rlJtHXyj8z2v/VkK/ezjWWL6bPhp
+BXmpXyB4erVZfNSDeHHNJrhs/mM4/bz+nguliBg7bB7eKs7jPdv9Gjcw4OA
Ekp2T5ARTKjS9gn2oXh4/v4feZ1tMD3nfjvuaSgCE6Sv5Xzqg3l1/sIXm9MR
LG9wufPJcZzXrr5oqfYXwVWS79brKsLK+Gf6kjf+CLEb+GLPxw/rq0GXF0yv
Q6hx8cd/uWdxoSpnPHt1KEIT5ZrXi+nBji/Qp+XoHoT+CRw5dE0dF49aflcZ
CsXjCLNtoZvFcHnShz550RCPB4r0Mx/Mg72VkOEOHyrCVDfY09kjcGhfEXhO
bx3COkbey0TW4upVtzPjnnsQLhGw8RO/N65/Puay0VoP4Vcz/B8fUoBLrrqQ
XFQJwqu6vjo9oOFGzrFVArxeeOq67b0i3wa4VW9Qc9pUjgha67bXs5W4rXMn
6kOsP55tng25t9cJd26Un+GoXMUzb/mR87dW4e4H16GouXWIVLqZIf33Erxe
iNOGOTOIClq7K+L3Utw7FmnZuiYUUdzDETe2Z+H+QsFbxvdD8Vz92oTRVUvc
L8HFmMyleD5Yniv0PQ2+qO0e9z2M6AOX9/oPnkDAFf1uixPlePkvS9ujJxKh
e7Q+3qmWQqwJ8/UpqX0ITfcXFVbzRWwq/wJV8yE8VvDXcdvTiritqdY3h9cg
bH18lPjK14jr5pHbfckJ4ZtLSmP4LBG/J/Ftmo0IIr2FZrXphng9OpL26pQZ
XolLRLc/nY9Eyfglxl0/8co6fjpa7goStY0u8Fv64lV68PF60w9IDM+WdLL+
hHjd24IdT5YiSfXWAw1HQSQ8OPJNwPQM3txZaM7wqUDSggNZp59mI5lfauHy
lB14L2lw+6crP5KV689VbKvG+ysXpTQj1ZB86m6++8dzeF9gZRSf3ojk5N6r
rOxHSDkzKHzCqA7v9ZO6UksGkfqy8uC4cAZSnmz/eKTtJdKXyD3nfdaHtDWH
TnvPCSDj1Oxw7LU2pB1UtDS9FImM2/JOM40/kea4/Jxi6wZkvFzkKxu3BWmF
XdYd7zSRwf4+8qIoD+nbcrIi3uXik7X8zM/oG0hv0C0YNvqOTDMN3quzY0jn
aGp0LFZB5g1z3h0FX5E+rlxUWuSBzDDpzZQdM/i4Rqzk2eZFyKwJu2Nu3o+P
Dqzyff9kkKUqy9rdXI+MZddrn701Qda/g/tfpnghQ8ZWz+dMNLLFrmYdnA5D
xi6zegcRDrIVVeO+Ojsi44xG4/47Tsg2i6pY0zaEjNRFtO8nApCd8u7p6sAg
ZJRMGdEXNSG75CNrldUPZLQOt34uXInsVpML7PkUZMw0t0duTED2lOMhE3NL
fNJ70bl/phA5+4ZOrB9IxKdzwRZbM+Yj50TjLtN1vfjk4tW9yu4ocqwNH4sc
4OBT9IWe780dyLmnsISi9wifhpV6I5NGkVOkHTa44gIyeWSt7p3eg5w6ce83
tu7IFBXlOi6/ixxG4FPH3yHI/G+yX/u2AHJ+n8x5cdkLmYFlgz+Oy4EiG1Sy
3HEYma/s1A95SoKy7czsyjU2yMxZEhiXKgyKWkXMi3N7kMk5vs2IfwqUY6fL
ttFlkDkx5pmyewSUU8Fl5xvDkbXsWfMCm35QrE9Lrzzvjqw9zOs5JU2g3Ggw
Lr1LQ5aBd4XwjwpQ7roKqGupIMtGbuVlqTxQfItq+4v/IivkSq6UeyIoEWrP
jgYVIitRaMmNpOegxDjS0kplkZWXYdHQGgrKa92b++c3Iav/7z9vZQ9QPvJ2
Nd8cRtZ09LFOSydQslmS9ZqPkL0cr3YG2YBScLkmSPkksuU5v4LyzEEpTSpP
v30G2Xt9tfsHj4FSGT68fmctsk9sfoqVOqDUqip2D4wi265uIFJHHZTGkFup
O6aR/WRFwNG4DaB0XN73zmUPst9mdyY0SIDSOVIX88Ye2UXmW2ZmBEFh7goq
XRmO7JbZOycV5oPSqx77ul8X2V/jGtJMJ0Hpm6dwZEQe2XM66/gf/ABlINis
l7IfOaJfrp0n85wy2GsZ7G6EHIWHn/N6GaAMzd6QvZyGHK1toqJCDaAM93Uz
Dx1AjknzBQeNMlB+RHUr8foh54pLduUVCigja4ov19OR472Kf23UB1BGb9Af
3fBATkT+KfeqBFB+vbo7xjuOnBTL5OY/kaD8fi0kXhmMnM+8M1vWB4My5jl0
uCkaOR2J+veP3wPlj6qrXaUucr4fftnj6U64Xjp2rzgo876N7E51AGVc20DK
/w0oq0L2hXRZEY6+SV3HS3K0I+zrYjPCXWKzd+6Cot3Wt19VH5QJ3hf7EzeT
3Nzc9eLCfsIi9+cOSIHiJOU79mQPYeHjO+/6gnK/mK5fupW8P+u17Sw5x3Pr
zUk/ZQl3h+usfARK+sJbPNKkjvH05ff6xkGpeFd3SncpYY87DswaULr0pTNu
ziOsafnW4wXRZcRJIGmC1P9vb9asJnIXPimxaR0mXBD7rloPuVKqy4vmcQjf
Fup5noTc7Z3W4sodhCGWlN2L3EN3Mq9a1hHmVxNYPQ+5Z2QWVAd9Jnp18rqm
vUOuc7mpbF4O4ew/VwM9ketv9/bWYArhV88N9RWQ+3LJZNvKeMLR13+HjyP3
0wfdbTrPCCfPv/7mFHKrj0f7OQcRrqvtQgNymWPf2XE+ZL9Fh7pfCiJ3LBJq
DW6ELX77tZYgj7+6P2sbyduf8op25VzkSU0HKT96Tc57OIi5JA5527fueP+d
5Hf864ETvAnIO2DJ2KjXTPR9+1XosjryToV6xqdcBOVvgOM3s7vIc/gsv0bg
HyiTQTWef+aQ5/27LupKOChTmd+mNk0gL0LuumjtFlBm+Iq/PLZHXrKpRKgC
Of/sLaX5vXLIK/IvEXhI/J6TXrM0XAB5tDxb368/kMvzzcF3mQ3yBoaXzTvy
ALnzvkw+XdOJvGnpT3feSSF3gWhU9T8K8oWOnZrkz0DuouvrRj8aIF81I+ln
FQu5S+tXWl89jHzdPv0rG12RK1Qn3PznIPLPif0e8FuK3BXzl6zzW4F8l0PP
zw/EI3ela96TO/7I97+p1XNQDbmScq2R/ySQH538xSyxCblrVsyPEdmH/PTu
R60LbJErixHmyRjkM9BZU/4EuVvOuikrXkH+92veBzcQ35RNNM58sEIBb8LG
0nslyN31WDxd+BsKFBa6UPZ/R65Wr5jmZxsUaO5ZvTP+PnIP/lWkWG5HwYlL
pWnzJJGrb6F1v/k7CjzqBRNLDyHXYsnvTXnBKAj+lyWzjolcK/Mj4XquKEhQ
toj2ckHupWkBFbMVKKh98vYJXiHXY9fA+xf8KGBVHBOM3YNcH5rbfJLXgt/j
fwL+kZwEVpw9qS2KQinz/V6F0yRnGZVFRgUoVA4cnJEOQ+7bNDftu3dRqFMY
4nZnE8ndQo5NHx2FDuu6HfeaIJdaPbit4yMKC7+4WuSlIfdv3hvahVIU0iSk
OiQPIm/BG6vtJ11QOHC07MTNbuSJ/OHYLnNGkeAH4SNqi5G3LZ9vUXcpis66
JO/OsUbe5QmoJD1G0fUkw4yVU8i7xTcQNiOJIr+Oia2uocgLdB0ued+JovT/
dDbsKkRe6uO4uoHPKOblZS7PFEfeePwOy7pTKF7ZZzwddBr5AkHveBcroFix
srbfJh7560aLndR8UGwWmJsrpoh8fUURPgnyebrY03Ou+5H//pygWmoxiiv+
Lj1qQHJQvubdfIY5irs676nI1yO/5+TEZY4JSvgaKfe+paBg+U55s6u+KFEK
TzKN3o2Cu4E/wt/Ko0T9QW+d/ykUvFiSetXBGSUH3KT3udxGQc6/aB1OEEos
ToVv0SslPuwv+DWrhhK/Nd7/ZvVQ6CQzKv04AiXMt2eSLM+j6Bbi6lQ3oeRr
VNTqo/dR9DLs+aeOIZSMPWwN3Z2Eos+HnijyS6N0iYOuh+Awipc0zXkH7kbp
7h1q+sWuKI7bXhuWFYLSRwWif9aRfR109hmG5ePz3sY6bU42SouPHPyllovP
hx6Neh9uR2lrgZtCSTo+n9BbWfRhHKVDGpfEwsvw2Y56Xu2WKj6LWScPnqjC
57CScaUVFHy2X8sfxDTB58GMdZI6uSiTVCO/lRaiLDz8+khSAcqvqtdtUglD
WeyJqG1Lu1F+f5ZqbtaOsmThoivOMyiPeqNkKymCsuJH/APQQPnnt5/qyPf2
sqEHMV0dRahYcehWbIkzyrVcq6r4i1HxYWF6FZOKcl2V7/Md2agoSdteTvFH
uclvkX1tPKho2RqWkuaK8itOpwteaaFi4q2NPb0P5RF2oxlqJajUvOvwOkEM
5cOnVsdc/ozKz/9uazWWoXzc8sqVr59Q2Ry171XlCCp4rPPVL75GJXvBKtb6
NFSIOpp32D5A5YzB7l0fslGx997z5VaHUbXjecUC3QRUHPT/yupVQxUyHrNp
ZqgwDFb7cE4BVXqRlrQH46iwiWToWi5F1YW6OpundqgI+rDqwalGVD1tbuOc
PIyKiE8XjeglqHp14tzrOg1UxFEosqbpqEqJFf0ZuAwVmWWmxSZhqPoc7eT4
tR8V3fSIyeMnUTW8Yd+MzSJUDPQMVDUdQtU4n+7i0EeoGOHujji2B1VzqT/C
7BVQOf97+059CVBFbNctN9ZC5VY+MYfD3aDuslmq8s8Olar8F/6rqgdV49Xr
NU8tULlvWdaSg0WgHnj/ZPvcblSarDJ+oxMLqomc6qZPRIez0q9vlIWCevqp
2dSqSVRekh3T2e8FqjXtfZVzJSrvbH3Sq2UF6rWsPz/65FDpt4ObVmwEqvtp
nzjOc1Q+3rPzrqYOqHebL48EEV8S97es3isHauDGtFTnDFTWm4mYqA6C+iq0
7EFyAio7zlitz2aAmpRZvmGgFJW9Vh9/7aoB9X3yuSDrBaj843A8ZOd7ULOW
2vqPB6JyzvnVmYxoUHNv0p3Xt6Fqsduo4vYgUAvzxjP2/IcqaZ/QaiVHUCvy
bs4O30bVRj/2sw9nQa32WNJUZY+q7Y+UbbcaglovFHtlNBVVB5418W3ZAWpL
sfkut4WoOhaztjl5PajtnfX1gStRdSreKW6zKKiMBhZ7/DSqHFKFNOT/gMrS
TvrvAx+q3B9W7edogto7pRNw8gWq7l30PBzjC2qfL28zUwRVwQdVDcwaQB34
0qJT9wtVUet/GouuBPXruk+Lvhqh6jXvm1ONlqB+2x4neccSVR9YZ88+TAL1
++qXewQEUZVbKH7hwA9Qf7Cy8q5Wo6r8eeMV3t2gjtz9fctnJ6oa3f2uFtwF
dXTqYvaqcFR1noSrWyWov40UBl4+R1X/zonbOwVBHXto9F4yEVUjy9O8f5iC
+ucVT3z+LKqmftr5vYsDdTzSSO97CagL6tc+siH+TFy7+mXMBVTh5I4n65RB
/bvV59iqHlBX+4dEdrkTrv9Et6GDKm976GUEeW/SaNf2P9Ogbteee32Cn3Cx
mubXl6DulclJXkb0nhL583ugDtSDc05p1CjCx17vPMoH6vGejVn3OIRdPd+O
95Lc5bHyoUDYvzKxpRlUu8hnJVPOhP1yp8akQHV2PVaZlUfYJbrVJQTUO8aL
6q7NI2yYGS40H1T/7cU0xaOEpQ+/vyQE6hMht44vYaSernhXWRlQY74r9cR3
EX60bEViDqhva75wLTcQ3tGmVVEB6qe3sV8l7Mn5Go5sl5kkubERGguZIXp8
u/5E/QiorfuqpnRJviec6s7ZER1Ya714FpL8jf8UO2VlTnTuHBG4I0305VYY
2GaDOkd5u3yPLWGLVq2yraheEnFu5e8P5LlW2Rnvb6hed7xJ9jLJz++a5oJH
FajeouS/SY7k57du5/kPk6jevUxrK5vk5xft+ufnUajWGvq7M5rk59fZ0U1i
oajWpaarmZL8jP5JVNhDQfXJpIsQIfkZDe/1/2uB6vP31+nUk/yMak7ML7VC
tf15+tGA/+fnzy5VZRaq3RBqqONJmDJ0ZegRqn2kD5vMUQkHWt8Ma0R10DSP
Rb4wYYdvz0eCUf2MTjnvakb4fN3h/xiojs++ared5Gfkor5wzClUp4Zvsh8m
+Rnx+XSd64pqyjW281uSn5GM/QXXLqG67FikuzXRbeTvfwz7ElQ3bDW8u4bk
Z9SkR21rK6oZAvz3Okl+RuusEiZ2opo7WBLwlOTn15kFKyfno/pHpXuIYSTR
h38qNqEf1ZOvlZ8KkNz8bnZVNfRAzXzvwedVJD9jOW9iNQdQI3Q2Ls6H5OdP
Qf7e39qokdQwS9Ig+RnvZYz/KkSN3Grh95MkP383bV7eT0WNEn7vr19N8uBW
6PFeHzVqNm2MVyokTwPrveKuokY7gHL1hh6oMy5aoaJ01Oh/eLHoyAVQ/8mO
//zwGzWmLXdeSpN+nPst906lDzXn/55TGY1ANW//W+c3Yahx3S9nFUVF9cJd
i7iOJajxsls06dCLav4nDx/6k/UfBg6F7ptCtYB4qljGXdS8bEsrHFJEtfCT
P+viq1DzdirMuOgAqlc8io9yeYOaT2tdvoVZonpl2lwJ3yRqqi6pS6iHoFr6
Wkp96i/UNAdLpQu+RbWMiM262g+o6cqYO8ghum9gRrX68KLm50y5y8NfqFac
WVvY0YOaKZk3AmcFUL3dINNrqT9q5x8MiN+5AdW7Gg2fm+xH7apQg8auk6jG
6T9+q3+gVjZru22aE6p1rkgPr0pGrWLnitl7/qg+8i4oXXEeavetZ2zZkotq
49xDV+tnUXspx9r3thSqHbZbpapIo/Z690Fpw12ovt4oHHXTALV3eTdlbjBA
tUdcRILxK9SGHf3eW+eJan92mE6IO2rzmO4aUhxUv+keFSgTRG0Fn3nLyDSq
02W3vl11BrWNmzQuV4iS3MU84LgfQC3XeV6kw0FU16hq/+ZEoG7pgqDfhe9Q
/XOq+9fjQdStVHB6+PgzydEfvh27XqNu3bETMhc6SY7kFSg5I6hTiRI/JrgU
NRJbfbN0u1B3RvFVsiXx6UDjTW0fLuo+GGWfI/dozbuDu8PfnUMd5YBPib4e
arKtVv9xZ6Dus+qxtS+sUVOWHjG67BDq2iW/MFVDUcPsW+LU3YS6WY6EhdNX
1Io/n/2++A3q9a/eNmFHo/bx0PIn71egfvjR/qOfeVGXtLEnbvFV1I97CiYL
ryL7xJ8sEihAA8/VrsWW21BXuzdvK7mPGkSNr1dNmaNupH5gl50cGvauTjyw
IxP1GkcyIx/fR0NgMj8SbFHf2bP5+gUWGhUqG1Tu16FRJi3Nbm8wGnc9nlcr
pI7GPauldRtK0KhloXo+6i0aDfzuBEdGoNHkZ1zwh3tovHUm75n9ITR6r3Ie
pJPnWzvTPgwZorHjsnjMlrdo2j+uZ0PRQSNHRW9n9ko06XNz+WZk0Dj8z6tG
6z6azKoE6eYDaOI94jKdnI4mR/tvoUsIr+xhbioORFPU+r5byyPIOgvTfb7u
R9O3nNsWu7TQdOhKTcO2m2j6k6ewvEQaTXpN/RLXyftz7w44NJujyfSFRNq/
NWhecfTNhw8aaHJQ8ukRmUSzWmD94IY6NEWamajuTUezd4yTpW4+mmIKnXy8
v6D5oWLkqQuaaEqQDaivIu+HxTEjupejKXW4yOZ4EJoTVI9LLdqHpjLvjY9t
L6K5TOT8zd32aPrxbvJb6Fo0z2q5fPnPCU2/M955ni8Cje/h2Qq53Wj6m39q
xU5L0BbnbpSwmEDzvDqKens0aGLldTKiJWhe+dP1ofQq0BQfh+xb/hLNq//K
S//IAW373OVAlc1oluFp+1hyEjTV41dumuiheYuICsP6KWj7XuVYyJ1AM1R+
b0oWAc34N9+GW9No1tGIL7j1EbRT3vfnq+uj+cjBE4b6hqCdGZMzUXBBs5Hp
R7eRENBsH0xXddSj2c7DqUp1KWiuZ/4cclRDs/29tRb870HzELK+ZO6I5muB
DT86j4J2JzF202IzNN+K2baS/I6m3fdecimTPB9SPHyhfAFooX9Fd72MQHM4
9cXk09egPWnVUpKsQnNUs+4jOx3QIiKeRvv5EB05yVlLfEB70RCz+OcVNL/9
Zn64Wwa0lzoVkdv40Zw6trg7tQS0uPj57+N3oZmy4NJ8w3+gJYo0Wm19gOZC
wVWRsjGgvZHvL9BTQvPnldQtY3tBe7d+48wFUzTXbdpo9OwWaClt56xqyf7N
yu1fLkmC9iFwLNyiEc3tar631PNAS98y8mlrEprZR/vje/6C9mmzq16tNJr7
jZ7uTnsGWqZf+k4DOpqHTuvUeO8GLaspo/4SFc0/bcYsT7SDljO/qzaTfD7m
kPBrww3QKBsezmVeR/Okq9GDcVHQcpVlTzwgufjnySdRlQla3qYF+cerSS78
MlKjjEDLX/piV7geaPyhVvsu/yLMPJoj8xC0ZVHL2/Y+Bq0g5q48L9FZ5FXp
JUFl0AqPvjIQOwSaePLVGVYj4QGZ9oe+oEl9Whf60RG0oqtOqmtJnTL5TRvu
LSP8dSp110rQ5Ms9KcYpoBUbqSpns0HbUq+kJ0/2LU6JuthEcqfcxmRNfCM8
/izO/Qhou49+DrHLBq1k1x9H2+Og/VecpNnhRdjmgovNHZI7lYAfh3QJ+9z3
cecF7eA7h5gcsk9J6KgdvQE0vTXH9eV7/8967BAp0I4/UZmJIPuXeKv5tIaB
Zsq/KmWh2//Xs0j57wNop2/PWJDf57QS9VOOseT/86PsJQOk/hK+ztvdmqDZ
2ZblmdBJfaX+4mZOoNl3vblUkUDYZelf03zQnA0DJXaR8xdLiWmt5wHNrcKR
mqhGzp9ncJ63j+RW/YS72HzCx+wElrSA5r9Bon3sOdHv3MSNakXQHkXO+tpc
IHozaSv6NpLcLuvd1Ur0Ljh5vC7MGrSYibfhnyqJP7uERaVIPZ9qVU84jxK/
K8yvyJI6crVW83IK/u//5g63SbJP5r+PJ4gvOT56rgtILqpfVgrvIDpk45LI
LVIfy9m4fvQwWadZOCb6BGh9X/bcOb+CsKb/K7U20IZOSyk2MUHL+LhMQIO8
/7NprlvrHeHNRknipJ4/B7iB6S6gfXy7/I3BV9Cm8qr+WwfCW6efb9ZFC49S
8lDoEpLv/Iqj59+jZcHr4Ki5VsInZD6MxaNFQML5iFMsaGmjn9t4W9AiHGzy
l3WZ8ItTNZUSaFnJp/b2mArhYxEP0+loWe0ubVo0R1ho40BEHFrWfeddtK2G
9FNn/vX5AmiRP9+X/ZLMow8Zs84ZH9CypZ1qK3iOcGTk5/Ub0bJdN0Xs7hbC
QbvLLJXQsrskpPz7OOFgzyMsF7Ts3XXd5Uwp4bhVvilqaNmXbLq+PohwadJY
5GO0HFqr3qJhSvh3vU7hIrToha/xSZUl9agq6q61RcuJxfN2SH0nHGT1LZSG
FtM7/b1BFMJjggvLdqLl9K/q0Bkyb9IdyU+JYrRY2aVq2esTnlVIT9uKFrvu
0J/dpA8+xtYe3eyIFofjLrG6HKK3qeaxXFO0OFeaGeSnEn82iN0dPosW9//+
+7fFncyHhWy5gnNouZO+NvWFNpkPPFuW25F67snxnSG/22jZwl53QlejJViw
Jn+IzEOKu+3DFGG0PLm8/tgzktfcGrfW16/QEllxi6ujSvKlkh0m+w4tL9e1
uo6SnBTkRD5J34yWhNtbl8QQvYuMQn9evYqWtx0PXh4NJ/2xWOh3/mG0fNjB
3D5B7pdS+j3JRUQfyteQU4YknxWV3zVK5dFSpPNleJbMu6qB9HCzOrSUxWl5
Jd8HrUaW541JGFoaTo6+nU/O3zBcdMC/CS0tGUf/Syfnb77Nih3iRwtjWXzj
GXIftG7+gyZftHDLjcZzSB8wuvclLL+Glq9rUx7a8IPWzRExu85Gy49bC9YI
00BjLxSQW9mMlsnt2Qcuk/4aeHdvzuwRWv49EmSIbyM53+wzU1CIVr5BO/sy
Mn+/U9/0Ph9Gq2DsqnBp4v+fC+ozX4rRumLq2sYacv9NWi/dMngNrRIm1flu
a0Gb9areeNIXrRuWenCaMtCyUCpRYlkZWtVu9my/x0DLKoZTUVEMWjXbdlUo
k9xLd2qrXwtDq45ysFmPPVpkp9mdz6bQavAFXqo8aNn6KqHQwhatNsavGoaI
bjpukUfVrqP1UtqUVcQIWo56blyzJAmtTgInxrXz0GL45lpZaBBab36eLx2j
j5Yzp4bfLnVGa4iSrb0hybW7tv+9K4TDHxbNzWqixdNgbUYg2T9qQPxJMvHJ
191NcH4NWl9HU/P5nqPl6ZaERS/C0Zq3ZMvi7FK0ZC5oik+XQWtf38830oJo
mdBf3DKzFa1fuT33TmqhZe75T5lr5PMfnNqzIWQffp5rCW4ctP5lv1nF2050
Ws5r8nIH2pZ2W/oPvETrXs20t9oKaFNpqb+cvg2tvu7b2ZxutN3//H6btj7a
Np7mL7J9j7aA0qglt++ibXubctf0ZrQFl/gOZKWjba8pzXFvFNoii6xiN4mi
7bjbKdneIbSl5EkKLyXr3Bbe4F3yGG2tH/1H2+3RRttSfSJ8Gdo3xNlmXQpC
+10hNyEBD7QrCPinag2hPcB3048Nj9Gu5JqcuOoQ2sN/5Uo7nkW7ut6P8Kp5
aH+fnLic8gHtxyZdXTbcRDvdR8dyrhvtt0747mDZokNJXefGm4Vo9yp8q5Bd
jg61wrvHCiLQ7rupRjZYFh06ikvUQwzRHjonKLK3Bx1m1FyBuzZoT3r/dPS5
MTq8Rs6Fpb5EO21+YrrJPnTUef29c14F7R1OVW8VX6KjzS3wyuJgtHd3fo3j
m0EH8/gW/kFHtH/5uDUkg4KOn+8HTRk30D57JstJeBvowmNehR/90DGP2mH7
JQj0VX/9xkVj0MG/c9KyaAj0dd2JuwMF0LFiiYaBQyLoytpDvLLP0LEpu2Jr
rRTo+r4DhvVq6Ngm80Uu3gN043sNS7PU0bHz0WLpmx2gW1gWskZ00aFprb9s
UxjoF1MnqpVN0WEs1Drsuxh071TP9HopdJzyGO87Ywu6X4TqpLo8OiwHVnWr
lIP+yIL7uOExOi4VnK7leoEeeac9jvIEHZ4X+95rjYOeuvrMRfUodNx3e/Ht
dQHoH6Noq0tH0BHga6TI7wN61mTqutNe6HiSUJrSJAh60Zk6OfUcdERmuH/f
2Qr6Z6sdfQtt0BFTqrz12XPQKw8fcHQpRccb5ssPZ+VBr89tO2DRgI6U7yY/
Pg+D3nzg0RD9PDo+zixTks8AvfXTpcXzBtFRIHEr7Ycm6F271zDdw9DRZGz2
8c5J0Ae6zakHUogv1kKjvUSvr3e4SYN70NF5rWqHDgf0Yb5l6xWAjr6QXZ+W
OoI+krtnLHITOr7GDP++qgL6r6HCiQU66PiR8npnyxTof3gG+8150fG3RiTz
hS/of7uNh0tJPbP06rE5PdCn4pXkbJpAn/fFe5e1COgz+r0eQXtAXzS+50Yl
HfRZVvHBPuL7svk/sxVegj5ntiY4+i7oIiuSxoNtwODJMZ3Y2gy6uKzl7l8K
YPDOVhYxOkGX2i7mZjICBt8W6qcvLqDLoC4nNwuM+fuKtrwwB13e4N5faQ8w
Fmgt/vt9FPQtZ/7b460FxsKNy63mSklurvxy719IeGLvar120Hd5vMs9XAfG
ovSxnXH+oKsHnJtMCQOD3zhpRc1K0BG5Sl3YjDCnxGlFHOg6SY0eLmvAWGyR
qXZ7E+hHsnzzOvoIF49FZ9WCblCuMf1fMhhLhMaHv/KBbkT781/sVcJ6O2I0
ia9mvSm3+XYTviGjolwP+pkR6wLbGcKBmnhNdLWak5yp+Uw4ZNHhRqLXxWU0
jW3+hL2mq9iNoDtIBdwJMyB8PkbcJwV05y1aheT7MmPJdseL0qdBd1Ob+Heq
k9QzMpbxMwT024fTNAvjCMdlp4yZkJyb2nrK2BLetzf3eSHovrbSxQ8Uyfla
hHuOvQc90KV1bvAX4ZNFaV3hoIfeC9LSoxB96loMnhJfn4Zpe6XfJbyrx+CK
DujP46ZKRXWInmH2qeUfQI9Ny+B1X0L054pU/lcC+uuiS/u6mghvstLcQfri
Q1fH54TTxL8nBoJPTUH/NBTCt0gWjHl5YmnTpE8pkwe1Lw8Svzt65FZcA71s
ZWb5DuLz3FR9gkga6NTHcetUSH/++/bP/g/JS8PSwNu7zUie2u5mC+WDzphn
paL+H+jT4X65LiS3P34Ivd4/D/Rxerz4xyTQxy5O82iPkfzGbz3/MxX0Se7A
6QP95O+XDedLTZIcMQpFj1BBH50MWJFN6pSsuHz/ONHxu8Lysb2bwVinZcI2
Iv3/7V90eucrMOTy9+01cQZ9iC7ZZkV8V/4oPnaK9NtgjORvw2wwdivyGVoc
Bv3LQ2XDE6/B+C/pR8oZNdKPnmdTvA+DcTC6wuY86ce+BwpfLqwEQ088vcSa
zAfuM6MPLT5gHA+LlrrAAzonM108aCkYpsv83G1/gd7L5GtuPQbGaX/n1otc
wqLLD3sywLDis1S+TOYJ2zQqIO0lGHZ3jwTZV4LOendaKTsVDPtJlUFHCuEl
4kfll4Ph7LJO52oy6EwPv0PzesFw+ykQ5xwNes+0bffmh2DcuTQ+4/KI8CPH
ETbpS58+jpkr0b1n+0m/aJJT/7P1me5XQe/+QnszKwTGo85cYQ8rwh8jDk+Z
gvHE5LX9bWPCISf+MyY5i2wKod49SNg7S1TtABgvdW9t8FIlHHBllVIgGAmV
tl4+pK+636yR15QA492+4933JQl33UiwOAfGhwKNPb5Lyf4bV9qS73uMTNVN
4X7/CD+Mj6c5g5GbsWIkYIScZ2FuR8QwGMWKc3qBvYRf/M2V3Q5G+Zuht49o
5PxHJ9c+vQNGjWz7/BAy39mix38XED8bY0rPPc4m/PeZVCwPGG2rUgqevCX6
/j3lYEf6sPNJ5KqnpI+5ovJPkg6BwRa85/IskPinF7Dgez0Y/QGOTVG3Qe+P
X/SrYQEY3+abK74g8/SL2EZlJbL/nynlvtgTJC8ndTriFoMxfUNK6xXpo2E5
tVe0O+jkGVkUnbCL5HZFvqWWCToF+pnGb1aR+XtcIXOhCjqXn6tOf7eE5DVu
1GsVB50ru7KWJs+APrF8wj9lMTplmgPLP7DIvD11JLJKHZ0bdwzP/07m8Jxs
+cqfh9GpGK53QLGE9NuydBOdAHSqmi6tSCbzgf+ImF1ZFzr3UhwWfA0FQ+D5
urNf96Jzv0T9wU3eYAgtKzVYUI1Ove5HlUlWYKw8U5R8fzU6T2j8WNh/gvSJ
evDSmAF0msYaHNqgDcYadYbGtSF0WlkJVsVvAEM+KXryrxs63b6EUMlzDDWl
pXxT0ui8c3iEv7sdDE1Ffr5lh9Dpk2x4ZHUVGNr6AQF9K9D5yEG4OuotGPr/
jF4JuqIz/tfjmqeXwbgg/uyA70J0vjX6taTVHIwrak6jAi/QmZp1QneFLhjX
PBvMeoFOirtI7WOSu7s360aHPNFZP/ukLug7GM/X5ucqFaCzxXJsaS0TjFdW
NWvXED3oJcb6SxrAeFtttP+HLjq590Tr/T+AQeHh7b9ogc5J/qcN98k8py+T
zfoxjq4NK5413RpD5xobXkH1Z+ja7PJXOK+P6F74dr+dDrq2tZsZTrahc/uu
j6V3C9ClFrWq2S0bnTqeshLFseg6tiaKdt0dnfaXd4a1CqDLY/OL1svT6CxV
3ChCXYQuz22Pz+w2Rmfttaf3nm9H1/2dvgO8Kehsq54dXlCDrmCNaxORlugc
+phssI2CrvjjhyUrStElpu93qp6sX+M+dn6dH7oc1C1L7NnolqTqfW9fge71
lI6mm23oXlu/3/WVPbqV8G43jwK6N9BU5+zL0a1euV/zv+vo3ta9fjmfK7qP
N+1UdC1E9/6fkyrKDHR7ln/dv+0Xuq+IJ3oExqK789Wm8QSybr7tv0X7tqDH
r/TZza9H0F1C3/g+OR09YX0O7k9S0F155LihqAp6Yn5+abgij+7mLa8jv+xF
z6eilVw3JXQPjOgqPDJAD1NOLKRcAD0iNyP1Gc5gbn264lxWGHrEh0p/7R8H
c/eE3nLBFvRIW3yLSLkFptaewl3ZK9CzSVOT5XkfzBOmNt33XNGjOa//mlwE
mC4TNkcuLkHPpaAd4ddywfxkLylab4gex9nTe7o0wcx7bHzk2AP0uDg+6NH5
DGZp6OLBE4Lo8TRkyIvXgNkosezYnaPoeSrmmVPYDeagsceRfGH0PPd9d3rj
OTB/aLmayf1CT+xEC09oP5hj89MufV+KnuRO+SPWP8CcEwu9f1AOPSUv67qW
8IC1wkzSNO0ReiqFxj2v3wdr1fyvfb8n0FPrvW59z2KwpAJYZ15Oo6fd+rp9
ughYclIB28+/QU9Xa8xyiQiwNis4VYQsQ0/vgcqse6vB2irM/pS2Cj3DmyT+
ndwAlordpPJLc/SMRmnHF78FS5X+d5WkMXomljgc2rwVrP/WK8/79g1M3uGS
kJndYO3TURR9pgHmojNDKhfywNJZba9irgvm0sYV9EZNsA7W9WjM6wRT/KOd
TPwhsHSLb91uvgqmVKW8YKQKWPrd4uuUNoEp09k3HbwOrGP0hvcKyWDK/0wY
vL8MrONZ3/KO7gVTcb5V280psIyu5+8UawVzu4TMZ6cvYJmIPNJYsIH4upWd
dqEVrJNhWeriOmD+tz822qIELNOxgGIxceKzqWXA8VSwTu2xCbybA+YBe2nX
Q8/BMreM995A1jvq1W2t4QuWhV3CC8dGMI89fWG48zpYp41qBgxIjoyTzTU2
nwPrzPq7Lr0DYJ4qllBYq0+4Y6NpOWHLFrq4mDpYlk7bn4isB9N68Nl8AXnC
w0tFxZhgXpw1GeVdAdZZg01JGSQ3jiKiPRPEz7NPp4fcFMC8Lt9SMzxMuGz2
kEMFmO7/heVwGITpSZwoDzDvGB5/Ta8k3HojTGkBmD4XhB83fCKcM9h8TwRM
v5uNd8vjCN/zyfx4FMyg4OAreUGEVau6Zom+jxP0zdJvknraYPv9HZgRlKUH
kmwJn3b+IucJ5ou62h3RJ8h56n+c+LsTzLjeh2vDQFgBE0UhYCaOH1nqr0j0
uPb3yhDJ+XuBRZN3JYheicleTICZvrZywGUh0bPim4r3BOmLIzolZ1lgmTW4
jotLgllsyZdqUkf8yBk/9eoimOXOn5/rUohfofaD706D2RCt5aIaBpaxcKHe
B0swW9Lnzm/1BOtEbufd2QYw6RVFBuvtSR6Mb7hdXAsm5+feTUIHwDI4V0i7
T/IyyDcttmAHWHot+c/5Sf3fV+XxTq8heVPvaGyaBHNiv2rXwF+wDg2ubq4v
A0vg6c6QovdgaTV/1U8m5xZ+9+t2ZiRYmn+/hFP6wRIr+ngpmfSXhoQPR48f
rLWDStoRlmCpHbXaN+JD+uQ/hQnH5WBtv5tYpJRCdOmVPSvtBpZMc5mk/Fmw
znefVDa0Iu+NFo2pnQTLtuMh7z0DsNasjPi9+gNYV+tHE76SfEheC06NJs/f
zysZzCT5XeF5ZVMk4YCssdwvJL/LGeLTvpfACv64KVCS1Cu8d/KXjBxYkW9C
t3qROpbJzdy6dhqsmPiyf58cyblSLh+f3gtWfMxE48ApsJbgTUbnbbBSws86
6ymDtShk7bg2qftjyBNtTymwFurFHo9rASv7YZVoxiKwFki48VNqwMp/MNXf
9wssvvGD4gLlYJV4b8sRZ4I1j5sseIToV3Hbyv8oeY6Xg4URs2DVuEWcupMF
Fs+v2ODRfLAanWsU0kkeecRsYvLJXGl1mJ3mBpF5pivnbU32Y1zaXr/SHcx/
4W7NmtpgMW0uvDxiDebs6E9Ld+Ij92yU020DwjZr5PYWgTVoXq+Vpg7mzLdw
TZ5YsL6f5F3OkSfsz2qYEgDr13EVrthywnuDZisMwZrQu5h5aIbwIrnePaZg
zRyKfuAxCOb01x3XyZxg87y6uOXkEGHunnvNL8DmWztvxQiZx9N/8t/RF4C9
IPrFTEA7eV9GQ/WIENj8krv615O5NmO7d4uaINhLnjXWF5QQrtglx08+XyZ2
KfvkblKvZrzpq/NgCz3he/kzhTBt+vaYHNgiwjF+AbLkvD5Z1UljYIsGq16V
jSR6GGj3LpIAW1yg2axAkOi1W6xapQZsiYAr+0xI/njVI1nBi8CWWrRg849J
ov9p1XqzRLDX3I8V8Sd+870wv526FWyZeXumZfrAmv/XdlnCdbDlZu3rjJvA
4l9WtP7jKNibbi3M/HEQrMWVlVG7x8FW+BsX41dA8hKrVOhoC7bS71bHvDdg
CaXdOhceBfaOa46mxiQfywd5R15YgK3ykx/fSX+K7tuOGQ+w1Yb2Ll93FyyJ
k+nrN1qDvdeubTJ3jNw/Kx42mYmBrdnvxDG6TPL+a8M5369ga7MTPvmakPtI
zHfo2zGw9TsETIbJPNkxNRZF5ifb8GGxnjGZB6rrjgo1XwbbSPP6/kKSi/+c
lFeapYNtltilFGxO7peHZjvGzoFtcSpEbnwArCMnuQ8/E/8sl2lLnXUm80D/
8Tc3oqe1y/vFygFk/uRmnTVqAdt2k+VclCiZd0r6Mj5UsC92i4zzknxaN+pr
zx0C21Hbg0Mj+zsFR3iEXwX7psjRAheyfsDid9nBIWDfqviX0UPWD6HxpRY1
gn33Zsa7AyT3EeW2j/hJPfd6JSPEyfqJ8nm3c26AHZw25JRL6i/r/lQyugbs
1/oPZWfjwJ5/xWP8swPYb3g1JWwVwV4skvvruxvY7zJ/CTXkkBzVNQbf4gU7
TerUTGwDyYV7/IF1QWDnftvcvm8W7C1vbdindoPd6F8d4GsOtunW6wNXyPNT
5fwjQivApoStXMFKBnv2iN/DQhrYRU/3s/xJHucaF8rZh4FdHpvVWn0avfM7
+cxrRMBuql7yZf0K9Ar+nK14QPirdejSHTPoXb/61/NpYfSutu2uz32JXt3r
3Qe+LEWv16I9nYJJ6NWfNGc/rUOvr8YGSeff6DW8y7ilE4TeIMcrrN556DUJ
aE+PF0BvZGnYQrYHes/GNq8+swS9H9fSb8cEovd6bcVICz962VekPdjP0et6
XCfQm4regS2L5DLM0eveXiav7I/eb+zwGw990Xunt8SC9EHvxJaDtRveotdv
Iq/yyEJwlu2asUzfj97o9WkviueDs7urP+7AY/S+ZB3W2dsJzl515fDoG+h9
9Zw9nJcGzj7fZM3GTPS+ERHRyDYHR3eQ2Ui+//Vm8LiwUj+Cc7Y6s7ZCHr2Z
Bcv8t/iCYxPaGLe9FL05bknK5J7iXNLOc1m9EL0FPzq8E/nBcb4yxTLfjN6q
HvX10Zbg3Cv2Vf+6DL01kbQ6SRVw/JhXE1ju6K03vuISuRicwC+WjWWq6KXV
Rlc8yQTnSXaIVo0Jenty5+wCBcCJP9Dg9fE10eVGpDA/G5zEdKMLBh/Qy92u
TPHNBucd30fd4mPoHXxrtdjHCpw0m6fyUQ7o/R1R/v4mBZz8pex3qfXoHT9x
xmgiGJzC/H92j0fRO7nsz8wNa3BKjFz1olLR++/BRv1rguBU/Hcp1OINOLxa
xX9+9IFTFThg503e45sxe2mfB051eYnZQS9wFl8P+HnxAjj1P1M3vpIHZ6mS
7LMBdXAaezuaYuaBIziUr2UjDE5zQchGgTlwRM8PPz5bAE7bll+is3zgiEs/
UOsJA6e9pDbX/B44EgxpjoUdOHTNYBm9deCsNTy201QEnM4/hz61NIIjK/Cl
q3UQnO5tPmNnisHZUOV1/0QhOD3HldbsoIKz8Z6EYhNZj3nmxqKGk+AoaH5s
M7gIDsvIa09FKziKU0fv1GmCw955tz+UnFMpiyt/dAXh2VdDU0xwdly71VBF
1u/NkKo+9gqcXVtF3Q4UgcM5Lhe7UR8c1cHUtWXhhDv/rP9O/q7++gB13yVw
uMcq41euBkfjLPNqMVmfm9YxMncWHK3VbhIaooSnLzkGSoCzv0OoNG8InL4d
hX8vNIFzIOzt5T0lhE9K9s97B85hg30i2RGEL1TNHDUmOVzMyFe5QthKyOlf
FDj6lJS2pv8/r9vSTIkBx9DOc8RBjPB6jxQnA3CMVhoJLL5M9vtq2KxC9jGp
kJdLJDpxYxKVbYgOZtcntfb/vx4tavOFOnAsZOvMmaR+Totgzc794Jxpjr3h
8f/zGtftjlME55yXc6g40ae30kzJiuTMWulA8ieyTu8mgZJebXAuMFdVHCP6
sz329ZaTdS8GfWMNE79YhaaX9EkfXvmvaMqf+Mkcfb/gxjlwHIbCxDYQ/5ni
Mcotz8G5GnVBqXQ58U8pdNORx+DcmBCwmcwHp0t18bSEBjjuiUzPCJKfzo1n
8tnE11vGH5/vIHljCOjO+oqD45Vh2nhFiOQnLUGq9P995PBarZvkudlVfThh
FJxgKTdjd5L/JqGTKc91wQmtPeoktgychlg/33v24ERsGnmtnwNObdLs9F/S
53F9GoLFpN8qzh7LXysNTsIT4c0WpO6yIungumFwkvZxtSeywPksXuHbRXR9
HxtwU5n4XFQY0RY/CU62eRv31SdwcnoXXe8ieaptdqTctyD9Of5tuUMz2ddr
X8u6dHDearJ+CJN1mpVEvxcuIOsGpFy5HUnOEZQv+4fMo4TNTWu1SJ29hxc9
siN9Eh1vkPR5D/FtvPMtnxk4L4SW2Yl+BmcgMfVzbCo4UT7xvxuiwRnmM5qg
m5JzeR0eNCHrjhfFWR15T87NFbOzJXNrEpoyimT+hCSbcs8QPaeLu9iCxO9g
D5bcgkpweUrFz7SQXAapaYTNaoPLty9LKvsU0XVjy9UPe8Bd8PlEVyQHnIcy
W6y9ToC7pCz41JkxcPx3hbcv9AR3mY7iKq07ZL4dP+N9LxhcofLqjvUkB743
T/rxDYMrcsAuYkEoOA9S6R1hbuCKVi4wHiR9cf/nXp2Z7+CKH0xYURNPWKPD
vfEnuBJVWrRUksN7UXPfHBTAlTrEfBxCdLs3f3HX3qvgrqHeNnQm/eZz+7D2
32hwZY5IChlXEeZb2i7hBO766pwGVUNwvCPf/DBvBGl2k0cSDMIaFx9ZfQJ3
U81v3RkyL71Go4/5ngN3i+7jJcxvhLNCbNIY4G6t21Zd6kI4IMjfRgtcZb06
/4R/hB26J4cNwN1Rf/mQrx9hK6pLrAq4uwz4F14iefW6+HTT8c3gqjYkVuiS
nHt5+n0cmAeu+jHt+9vWE37DFV0sAu7exl5t4RTCvYPpSwLBhaEn7+9dpL6t
dE1uMrj7mqVK2og/3oE/a85PgqtzPM+TcojwzJUkj1hwD9LMNJ8Tv3w8fS9X
HgT3yIk/s3eIX/fE3Ifln4Kr2/Kk4Czx616Rx+6nT8A1MN5+az+ZJ/c9iv3W
xoFr2NqovoH49+Do7YP/r8fIxH5yEfHPdyuHd+0LcE3al+QMEf/85NbZ7tED
17zj4K404lfAsW5byWfgnjHljj0mfj28l1YfUw/uWbr3JxfiV2DdIseWUXBt
GIXb1Yg/wc8ZdhHW4NqZm4+sJv6EykRVOiuBe6nz74d/xJ/HhZcvnM4D17Fb
RbGM+PFUJUO+WA7ca6ebvyUSP54Jn104Q/S93uOU7E/8iOL1i5a2B9ed+X6T
PtE/ZkPcbROSr1tnD39RJvrHnsxquugH7h3WQJII0f/Vy9CB/9rB9emVXd9B
9E5yqhWc8gD3wfliTh7R++2k5gafdeD6cc68iiZ6v498OftoGtwgbtTa80Tf
jxLqRjfMwY0YEJb89ofcnzJNze6rwI2KrvoSQ+6DklcXFjUXghtt5Jl5bCc4
5epJmpeI369KfupnXCNzIHfI2ojkO+VFg5f7dzLfBoe/nbsCbtoJX32FoP/f
R9eiwqTAzVisKdG9hczziFpxMWVwc1xTP4HM5+9vzGRWp4H7+XjQwIJ+0qdD
lH4pTXAr+HUycu6Tvhzv2HuF6FtVNON5aT24ApK7HwhRwK1XtF9Vdx5csUTK
Ci+iD32Rrm5YD8k5dVsZNxHc74WLP65tA9fij2tRzVZwR66X3ml2AdfqhOz5
zBpwfyvcPHpvBbgXS1gqdlxw/z4b5A4cB/cG7ZuY9TT6+JypK1OI76GFl7ao
ZKNPYpPvbbUKcKsP6vVPzUefTjjfIaMs9O17dbjk0UX0HZJ6QNH1R9/hJnFa
0BH0HUnk36x9Gn2GPN7OQs7oM8heJrBzHvosbfafLfuOPjP6ykYRA/TdUoD6
bDn6HKQUTjYNoi/zwLjUz+Xoc3qdUkXNR1++ScqNheHoc96qtKckGH2fzzqU
D7ejz01TRTJdBX1NZ1XmzSmhz/ucBjPEG33D85h1Cwk/fX3c1kAS/TI3LBSz
n6IvUrGl48B39G/8uZbtvwR9z7NOHtYoQf82i5ovDyPQF1tpobDVFv3/Ld3y
/k8k+t4N2vxY+gn9RoVlQ7YD6CtSdL9Rq4d+H0EVv+pV6CvJnBooW4t+P7+r
onxe6CvTuGOa9wv9Qd+fJN5WRB/VwEctOQr9zzx1azfeRh/tauBswAD636dN
mOm/Q99AZuyDw57ob+J3uGH8CH1flU9ftKShv1VCaX1hP/q+pUjo3tiAfvqK
oK/bXNE3kvBk+asa9LPKL1hU6aJvKsw3ZloU/T+W/1vP34y+WUFt7+Wk/tEr
C/fs+4G+uYc8Nhtz0T+Wcp2xvwP98709FIwt0T81KGhP5ky/4FWH7NS3GFiI
pAaaHPqFhxWiyqYwwM/Y/mTwBfpX2H253amPAQFzj/ddr9C/6ux57YW/MCAs
um6HmAz6JbvWyEvrYEBEzzFlQAf90ie7Fu98hgFR+7MRP3agX9bAuPHcXgys
spYvZSaif0PN8gzXYAxIqvP+OrCN+HCg4WlQLwZW/w1wPumH/s2lge4JKhiQ
flnxhnxf7VfUOGyR64uBtYqlpmqriE+5CzQb6RhYFx+Q+CsH/dtVPssMbMGA
LM828fqb6N+t+N+gSBMGNlw3MVi5D/173vyt3SyLAbmAeaOKTcTX9VkfcAMD
8r4cZ18n9GvEOj82oWJgo4OQvKo1+rVWK7nYS2Jg03//q7i646n63zhRSvaK
0qASGUlJRp5IRSk7Za9KKDsyMiKlCIlCSrREmRkVkpmGrSH5yr33nDtdIZX4
Pb+/7ut5nXs+5xnv8Xwe1IleBopxFtM+3g/jyU6N54uBslfisd7NRqCqZNz8
nqwDlP2pJ1Y/kwDq5lV6Zw9kAOWA4HqeVi+Mr/az4lSBYp74/cfX5xjT0q8+
TwaKBW9e2+QyoKqq5lJ8zIBiFX2seKkTxscUPvY6I85+y6SseYpxgM1JtwGg
HAnpC9DmwTjQU0AMcXJ0Is3moA3GTol7w/E8R79DO9wfYLx1YuLhU6A4E4Jy
YbP4PS5e+b8Dxc2zbS71AMZ5yU0JikDx+H7he9FtjLW2ntlbBpTjjrub6yew
nkqJ9I3vgXJy8N/9HmOM1/q31SAOfazrL9Eysf6wq21ZT4Di9yHM9x8N+/Xi
mdOrM0DxP7DdQkoP+8lc61mM+Als5Wqh3lGVlik1HGwASojRU+ndI9h/SXGr
F9ivs698Zu234nwE1eab8Hlk1XjDhUGgKrzeSe+mA+W8ZkFBjgrON+7DzZoU
oMSWuCSUReH8NUe3ZCAeEws/HfimAFR5x8EQdjNQLtk9029ORjw9r6mPGgHK
FYGLag8Rn7LzxbR9gUBJ890uEtQMVGn7UqUwOaDkal3rXYrzEdZnWrwpB8rt
8RPNrHeIb2GZ3iuIv7tZuyr7tBH/H485fJQByv3fjBv5S4DKr2L5104fKGWv
9x/b9gj5Y5zzbx3OtzJ4zQE5MaD8Klm6dO4xUJ5vmNabRxxOLxdbffQ4UF5c
KpTvPAAUTomVk0Q6UNos5kddGEAZv3pBPFkEKF9Hnp9MRh68P1x8jIP4GklL
OeqfBZS3jmd5S9cB5T9jLzPbBaC0n/zcaoY8RrdTXYs4fh3Pm/t2E/L89Gl2
NdZZ/WFJOAv5ObXW5HvOF6BUkG/G3/0FykzPqu5YY8xb0LzD7wZQ5rZ3VhyU
AEqx07FjBUbI+7mNoaNVQLlzJHjPnVVAXVY6d6JNHih5xYXrRq4DVci1z/5J
IlBylr7Z+fMIUMXfxOmePQKUTMox5nwSziF5+N/yX9j3rbZCy3/jnAwqWVw3
nAs1uqjlGs6VnTwy2AGUi8VJ3d32iBvrnU0FN1E/3fNP858AqpZcZoKOHlAi
8hSPmF0A6vbbO+Q8BoESPnNwX0obUHXWDT1NDQZKmLuLh/hjoBoor/xEKUFc
+S02jlcGquGTl2fETYESLHTWxBbrMdriwmdAQRw2Xun7/BOo+3YUqGeuQZy6
HtphWwFU03rj5sZ6oJwx7xRq9ADqwV3j9gx7oJw+fNk9cz1QD71OZMlMIc69
uC82LQaq5d5N8cZpQPFN83x9XAio1h2dK86oIS96YNv+UqDamfuU3OrEeNN/
w8HxQLXvFjJqRf09lfnwCh/ixsGmdJC7COMV9MXn3wPVacjCTz4fKN4VvLx8
bKC6OnB5TRFX3p7GK25RgOo+kpEV/AljNZ6G2g9A9fLYrnonBGOhVENerPcE
ZaCpC/HmvVj3wcYFoJ46FWY3gzrpLWPRIRgBVF+WLEMR8ea9e5WaJL5/JqA+
9hD6jXf8+LIy5EnAlJP0uXiMRyZAeh6owWH/iu+jf52yvWCmjbwK/XsHul9i
/GNEn7YUqOExu/vnjmJ9KVBv/QKokYvGfDZNYz8sf3CuBgM1+uKFBRvUPb8t
/En+KUCNFdyYGYN4Pr3p08MqXqDGp7SrFHdhv/UzSfgM1ERx74ZBb5yHj69V
NepQ0g1B20X8QAmounJodxxQk2WfkOqI46CVCo/ykcdX8w6dP2aI8809esVv
J1CvreVIJiC+Q3faBz0eAGp6YdqjsjDUFe4e1csxQM0q7usTQF2LqDlR7/0N
qLc0Qr23oV9HtXxJOwlAza2Q+edCos6wK7ccPwPUu3UOm56jLl7IZnoEI14L
Df6+/A916eKKoPaFcaDeb7ptLeyIeK58fJ0P8y1uH43yygRKqrHtwi88v/Rg
vHiaJlDSt38a/qEJ1Gcf1z94gTqaaaKaRtsC1KrBEz2SS5A/dQZpI6iLDeOs
ja/DgfJo7vhQM87rtXdqPQv9u6T/vf27XKC+YWpayqIulXXWbFmBeOv4GRzh
j7pYt7R66V0XoPbx/v64xgn14ZMGh4I+N/CiOkgOdeTjbNT1I01A/RQaKC35
GigDutKyVPSVbwThuEwJKKMr9ZyuSAKV+DhI/clBvbITWD6Buj5/u3K+E3Gr
erxH80Qm0Hjt/Qta0H+1ToJKiSXQ+MVVTRpQ73UvXLeJHQXasoR7yVXmyKPl
K0aye4Em5Zsuc0cacbl/7qrjS6Bt1j2jEYL7xMNF8HiQF2hqP1V6/B2wLyFu
8r7KQNtSQgnxEQZqzewDRXstoGmvc6p3DQJqp7a4zpwv0HYLHNx3QB+oTJ9x
t5RioNkNKLus/YD/25J9REcAaHEBYylvp4H2duJ2i6M/0C7MeQ8sHwZa38Oe
/wIwn4tJHHnzZqANO+zRT5MG2pX8v8Uf0oDGenpI6VIJ0G68l2rv3QyEGK+s
f34d0IpV9vN+dgHC+s24jpwP0Eqq3putNAHCYWzw+otkoD3bbZPmqAqEx+S8
SesU0Krs3dYMzwIRNH75oOhRoDUkntMfzQAifW7FvtADQOv970korQ2Id+d3
vlzkCLSB01tfKZcA0edb9fqqEtCGZmv5T10H4otRQprpINC+ibZkMNyAoBVt
snrsBjTarm/P2H+A5N2ptuW6KtDITs9fW0aBFHCgD9uEAY1pSzcMaAdS2MNU
444i0Li+M+8mM4GUW621acEIaH9zRMmZLUBu2ZkvcX4caPMbs7bqyAC5PXTV
5tbvQPCUy4eHzQGpe329ydZQIBZ3qCz5/RbIPUExLZuuALHU5tlhvTIgTbdt
VTNYD4Tgd+0bkdlAmvdvKrmAdYnOGK//5wWkXXWjlqggEBJxHb6GB4A8Nj2Q
oaUOhLTw4YqYrUC6SK/qWQgAYuUGRyOeeSCPT+w9feoOEBusQ1z4bwIZIqmg
ET0EhFKP9gpPfB62Y1ZONAwIFYvp7jd4foRuq2uKJhAah8L2xGsCGfO1WUFP
HgjNdzpz/2UBGR9Rt1KqCohtB2af78Z6Ema1g6PMgdhpGqG80AHk5dSAhPcS
QOi16425agB55aFYUAEHiF17/+Y2YL9Sbs9ua3oOBLS8tFuN/b4WvO5yzgog
jPdEi0S7AZmulBjtsAQIk+Zd7cNtQGbUKnmYSgOxf/d8nIEakJnKi4c+hQBh
1tiol5sB5I2zKl2n1wBhbhjz888vILPu5Z5r6wLi8KvdpQ5OQGaXngzYeAsI
KwPeE3XNQN7Mup0i+xYIm/rmdXLKQN5yseL5dw+II7rxn8NTgczhv3lY7TcQ
R2v3ZAxNYXw5xXTIEghHHX5zHQeMWYdkrvkC4VzdujirCcjcLbPq8Vif2/bE
hhkljK0qbNyDEbeV+8LtrmJsfS+XuweI41oCW6smMdb6edLaHoiTZe0MqaN4
3mSvK8cYCJ8tl4qCGzDOCAiXXwSE31Mz574NGEvw0jy+AeGvLrhCKxnzDWzY
FHMAiMAnb7vTJ7Ce8u9cAeRJyOYrl7lHsN7e+zrN64A4+9h8j+VL7Ee/hdIz
OyDOKQvNlSliv2oUV9XvACLywfvnopewn5HHC1fXA3F+Y6r/GTaQ1xW8gs7+
ACK2yEL5gy3O47Gf58VSIC6sFx1TrwcyTfLDmcJCIC6tS7dlJgJ5NW1KpfUy
EMl3rEUO0oFMLjqlzt8MRMoaifYnlkBeys35ETUIRMaqTD0fecTLjlq1OWsg
MnNsf6L+kXFfTy/KQx5my0mXKhOIt+OBPBwtIPJkstfSqhCPqrIdIvxA5N+w
/7x/JeL1ZF57sDcQBVKyGQ9iEc9XNA8Uc4F4IJ6z+Lg5kGcue11LFAeiTCiP
PjYOpLt/qW95PhAVV5yLjJEvzpN7w8OxH9WCa5wLkG8Oruw13BQg6gXudLtF
AWk9XyBUUw1Ey6J71SOSyM9jTrMB+H5bTXS0EOLDkD6hXuYARKffURN9QSD1
Tjlq4J5PfBgU7r25CMitW4bbB/2A+Pw4nGOF8179R35AD/PjWFoot3YDMQ15
OuceATG5WIUzhbyZ4B0Smcd5T9Xz1yh2AEFviJnfQwXiz/r6vTGNQIxubozQ
Rlzz/9roofsUiLdEsco7rGvl7b+5pVeBuPv2xLWnBfgd60GP4aVA5N7ze5nP
C+Q6gfLNgglAZF1oIh5dAHJj4Inak5FAXD0hdl0Ocalp0jOg4ANE+BuHgA1c
ILV+l+RZ4HeDF75n4b5Gaj9N8jzvgbg7tMq0DN/XlzXgfj0GxInV9mOLEJd7
GY9EbpgCYfuUp+cn8sr0bvzAmxYgLC87L+9FnBy0c86b3I28jErOb8kF0rJR
UtVCB3ld2uKa7AOkTTBrMroCiN2sWOuxz0AeUe6oK9FAnTD1m15AHXPMOG+K
/knssFl9nI3vu+w/JqqDPN3GH62X/QxIt7ltgyeQ91v69+ZOmgF54jjp9UYG
daxXxaj2C5CnVraoctEfNvF2Fn1JANL3Y/7PdSL/18HhAmvMN1DXNi56MRBr
nYxuzuEcgxt/M7moa6v1q16NoM6d3Xfn6AkvIFbp1X7yeQNk+HuTN1+lgJA7
9qXQnB/ISBv6Fgusd8WtIuHUFUBGf7mW04K6JP0nb/NPYyBj3bWX6G4AQip6
/4aLh1A3aV8CS/uBkFRUUvHZBmTimZhvijgfcbLGlUAdTJreaJq9Hf2xP3Tw
DepWcuTbquXjqPtjn88230HdXBSwNjYTY+kjU6ldqJuXpZOn0S9F/FybO7+j
TorWz5yaAkKY8OAPOo+8znJzHynC+HJHTGoj6sLqxe9tbDG2/JOmgDp/q/DJ
zg7klbCh0yqfpUDmbbYsMsD6ha0PXQh6AWR+2YxoOdYvnKKawwgEskAnN1IJ
6xfmWNyyQ94WNuym5mD9IudERWNagHxgQrUWxfpFN78YtosE8lHXlVcJWL8Y
f5EiTx6QT6y3Ks9i/eICEvpu/4As/TSYefoC+piWefkXYSDLXCMXxpD3khez
toWdA7KCquB7ZAz7ya9+2acWyGq/tsEunKfMk0OpY/uBrPnpZ7wbdVM2Sl1Z
vxDI+gjxUtRXYuXZBb10zPcVT42cCuJFPney8IEfkM0ivBOSyDMFr/H8sHIg
WzIfOiYh/jYsU7sQgHhpX2XeNod4V/qkfFQK//9OOfs2BXVMbeZu390TQH54
tmuZQxD64L6959t+ANmjPRbyURHx2MRekWsA5OAe9YO18UDo6/hddEdd/9TZ
W6OO9cA2Ux8ldSC/WoYrFmA9exy2W0yrAjnq3Pz7CuZvriL7zxd1nR5+9KEL
LxCuneqjOnVAMufnJXrL0DdWNf70RX5zEgvP70ed9Ln5ZOcsH5BTGWw7zSbU
ebHvVxzvAjlfmsDHFwtE6rTQIosEoPNuVzkTjj5+I7N3oHU90PnqP3xmjqKu
Oiv13P8H9KUdcmWDyM/iE4ZZn+OALjH2zOUxDxAdlvW2vmNAl75zZoiJe0f3
wOXwhEKgyzppWGmi3ny+mLZuuB/oqwdK99SibzN8BQ0M6EBX7nii3I5+L65G
3Si2A+iGTx9MUhDHnnPaYt1SQDfyPeGngv5zZibadZMS0E2UN1L8UO8jxIu7
rFOBblZQNDQVjP7ycGvx7H2g22bee8WHfWnUdhEuw/N8IvKTFOqArsD3s3bp
X6Cf1nHhOX4e6Oo5HsbP8dd/avW5xyZA1zN6d7oV8wk9neen2Q10m0b5XMU2
oMe65VjhNOhJNh/4T88CPWtf1ioXGaBzRm5aSS0BerNEyrOcIGC8YkdGXrQG
ektzUs5cDTDerko1ncP32oPiLrrMAWNw2+2DtEagv+sNdV6fBAz2OhGvgA9A
H8pwFizJA6b82/UuI1pA/2J8ZEbkP2Aqa8xwGBJAH560/C9QCZjbQkuP4P/o
Y9YmtdplwDQrclStNgM6S0LteEMrMEO8g54OKGNezUpWCoLAPN+w+MuHUKBP
Bq0zuGAJzEtM7tvzK4H+q1dKcv8XYOb1treqmQBjUfrfpm42MJvvfc1wWwKM
xUbTJdu2AbPrYSrE2wFDgMvJvhEOzP7oUfPMRmAIW/0448AHTEpuj2t1EzBk
xbtW/ZAF1uIEUrlMGBgrX7cK7HUGltB8ZGWrFDBWBzZMPrwHLKk9iwol9ICh
2FPR6acGLEWVqRlpLjA2xpVUfQgElvJbrmLJP2Aob31wV/M5sLZs5wu/nQAM
9fScs9NGwNJ37FAf6ACGplGmh/1FYBnJ6QSRNGBocVMP1b0D1r68HcOeJcDY
aRW/4fwRYFlO3F18ShEY+rxRoqO5wLJrmm7wyQHGrvLQv8ajwHKwrawbHwTG
HvFTvQI+wPJoSTBf0ADG3teer049A9aJO1WFHSHAMA10ftQ1BSwfg0v/jcoB
46CCfaaGHrBO59wV32ULjEM9VjFpMcAKqLvTV/MfMCzjDvpMtgAr+Nb2kLXV
wLDZuveInSCwzuqKzZQXAMPuPzCqsQBW+E2OMgX7ezRdV10uE1gRtdfKrhcD
w9Fom2zkZ2BFZdevDJwGhjNXnW9kDbDO7zCg/bcUGG4FSpzdnsCKuc7Kw3su
w9Nq3Zd7j4AVW/aow8UZGCd4V7bxs4AVd9VadpsNMLzLpcpPagErXqnfkWEG
DF93kbzOcIxjFa7v+AOMM+JLL6m+wvim1kyFGjACMt6v6N+BcfBQz9RGYARL
pT+MKsNYpnE/+jcjNOuIzkYVPD926s/0EDDCZVe2vcf5xlYkKwzEAyPi1vcj
Z+Uxvyc34od2ACN6VSF1zQ3M329b1EYJYMTc9g5tF8H6pi4uUXAFRvxa9cX+
l4AVaVL1XGUWGAl3uTdkeYF1zonZ9OUwMJIUn29oigBW2C63v12qwLhcFFHl
jfMIoZqNoD4w8I5mIn4aWEH2lISyb8BIfcTXV0cFln9G2BNXxEu6Soenhxuw
/LLMKp/sAUaWulV8pTWwjv/hSG/sA8bNZzISjl04f6dAW50iYORqfrnHbwIs
l0vpBqfGgXF3u+drOx1gHTHeGxPrBox7z5Ut/2E/rLqrLx+4AIz7OszRB5uB
dUg1Iv3qPWAU64cu/ML69+z/9ffiR2CUvNK7dicLWIaCtYe+xwHjmeHCWlNR
YO3M/Ra8nxcYVcaXDG8tApa66j2xkR5gNJjlROvRkC8Sts4pgcBo6nIV+oH5
Cx+zrTUwAMabQ+vzrnwB1pLg4a0uJDA6LEteDL8D5qxSyNRVxE+vfcOf8xXA
/Jyd7c7C96nHf4Q1RwHzxknyTUk+MAjaIwGfaWBePaCWGvwaGIxTftmSZ4B5
QXg2+hsHGBN+08+93IEZYGhW+hv7+SdEYHrJPtQb1wsb9r4Apki8WtABcWD8
yt/c1agPTHG95aKv7wKDqSv0dUEWmJJcslRXExijrddYVxqAKef+gFDGOXbW
9RR2VQJzg5GCy5Jk7LNBoP1QHDD1eGTM3vADw3A1aLdnA9OgZoqmdx15ncWK
qTMDJvj3JVQgjzfJE4en+YFp8j2tsWA3MMRsy2eO9gDTonG5dkw00H8UGf+M
OwzM4+d5FPRngH7NTCNhZywwvbVHGioTgZ54dL2IJ9btw3rlpIq+EnltjSQT
/x/gHJG9chvQvSMnL1SrATPSYFpoNgB9JnbNfPAaYEZP9RX7LwBdf965uEUG
mLElFftp6DvbymeMZEWAeVHeP36wBOjrG4u81Y2AmfaXnK0igb6kYCMRUQXM
65UdWWrhQC7MRFkn3QJmlu/DbUW4N/1OuRsaOA7M3K9eZ67j/Y+VtF1hmSQw
86/vERKsBpLGTErjTgGz4KDC43gTIMduBahs0wXmg/qR8UAP3BM+JseexeeP
g17FEbiH9zsGLYvgArNkc95aN7zfdG8/Npn0C5hPxyJefhLDvcQxxeT5amCW
5xxzsMC9sKPX0vU0Pq+y1vn1f/9tvTXa9TgUmDWCMjcM8T7ZXBkq+iAFmHWv
p7We4x7ahDYijrh4ea6vW30Y96T/XNcX43mNfNHiDDzvpXT3ndxmYL5OUbJ5
jPnV33hU+eY7MFtkPt44ifXVubetsfMEZtvd8KENJJC1kbxX1ZcDs3OzouxY
Ce5lY+qRxCv0ncouh7sBGN+UUfBAn/uwKyTPBffemttxZhn9wOxuXz2yaub/
e5yG4WcTYPZZtq/9jPeG2lsDpVVDwBz4EuCeHY3fy1C5jPdA5icvuUK73ZjP
cP+U8EVgfmE1UyRxD38ZEbX2vjAwv4X5KXW3A9ng+1I3bQcwR3mlvVNxf2gq
V7UQxudjyQ3F5oeBfHPwqPbmLeh7UieZguJAtum9DagdAyYtX1y9vR/IzthF
axq7gEnfVO+feBPI96vCvgXYApNZ7lm+xxH3PuG86gJtYHL0hX7yrgFy4MgX
/m5fYHJbnm9vGAPy86/0k88AmFOHXc9G3QdyZEL+vu5vYP52L/89qwYkSbKV
tFSA+ZfhqF/Nwb2O0STzEr83H8ofHYz3rpl90TJ2qsDiu2TPw9EFOr9A6HvO
GOqEBI9xyRzQl5/+e6lzNbCW5j5O8GkCuqQGj85B9Anhp3MC1H2I3/pXr0rR
x8V23jcrWgZ0taSob/vRNyWaD19xfwd07dJ2z2n0oRUDBSLfbHDvWlLC138F
WApz+6T73YAeTEk8uegusDYkcuwzNgA9JuKpuv8hYG0SvXnLggb0KyeH0sW+
A0tNkSHfdQboRaavVBLRF3eYpa1vjsS9R/bj5e3oUzv7dI/HGgKd8Ngpua4E
fd9p7KHhIqDPLAzBFOa7O0B7c90lYEhrb7J+agmsA1lftpZloa+GiPSo9KBu
j2+A/DJgjCcKxntgPe7uAj8jfqJeWT7UUX0PLM9vjIf2OGdBV1f+X7hneA9V
ioqirm01yqDCLPpIl9FIbBsw4375CK96CKyLFa7RHl+BpcFbdGy0HlhPY3Ne
bFoC7Psdqk0SrcAq+3fen88M2A2a7sxh9PHKCA/F71eBPfjoe1NRG7BqQ1SS
b4oDR6A5818sBVjNJ2sdlskDx8dlLIDHEViDhwdmGVowsaJUIOYK7k3zq8V3
PHOGiX6dIbp2H7B5ukVmHZ7DxKjB9SEBAWDzXRCqXyICE8y1VRY674G9lFy6
y6kJuHwRfYcX6MCWrFowEVQEruZRvRCRfcCWOflvcXUEcPXX98YXWQJbbuWf
drc+4O59vX70CQPYa2JnDtQkANfBJye69zGwVcxZVl5U4MaZJ6qn3QK26gJD
UswQuMnnbqQ+3A1sjQqi/0U2cK/7vjpS8QLY22XHj0qYArfolqRU2Ciwd3SN
yb26C9ySng3HS0qArXv++1fv38Ct6pCSacH8Dce/ujQWA/cN8wTLswzYRtmf
1/kuAm6XTD1ldgrYJgcGx2Qcgdvz+6OS2RCwzcp6j58WAu7I+NZTNthnc8/u
TbJewB0n4npVtIFtIfOeePMKuPQ72WnrjgPbNqrTb+UZ4E6v216b5Qls+y3t
6q1twP1N7deIuQLsY2MtnMC1wJ13OGV5awTYTjeay+XDYXLRuSTyORPYrqZN
Qe3dMLnEuF3uhjKw3f82bA9WhsllVa9D/LOA7fX0xcyaOJgU+iCt6FIO7JPu
dTWdX2BSNMVzPikY2D5SNedCtWBSnGvzXPolsP3aq/XXJcOk5GwKdeE6sP0j
Kua6fsCkdEGTYeo6YAeplzWEGcCkDCMv+/EYsENGn8YqZsLkiv7PsjRbYIdd
LzF6z4JJWSdNayusP2JfMd+5fRjHujuwTYAd9fth64Z8jHdvYc0rAjum5P7F
j7/w/RyvJFYGsONdC00jLfH8lHfxc/HATpQoEFR6hN+X09uW+QfYSa35Xb28
mJ9+Ir8FG9jJ4Xkp0Q4wKfbzcvp97C9e4y2UK2BSZLdKqwn289rITbH+5TC5
fJ05V7IZ2BnpN3pjvGBSIOM72acC7Bsm1zM3v4RJvqwBBVecZ/avdLtBKeAu
qG5ouskP7JziayviTgP3z+F3TZ9XAPu289XPajifaZ6exSsRn3fFknM+rQEu
Z7d+0G07YN97c8npwlngkkLyy7SXIu/OXlyj8RG4Y56X/q49Cuzi4biCxFjg
9pXHGi+bA3ap+wGBMGHgvtvWGmqFeHtGlTjtnQPclkN1U13uwK7iFOoerARu
5b4NnPNawK4J8b2zazdwi9d76M8NA7vu9/bFGu+Ae/fGcKZuNrAbF7X0iCMf
ru60CELfZr9OStHhC0J+nNzZDWrAbhGyy5taAO5ZFaNFHTjfTmmq9ydZ4Lp4
dR1wzAR2n8pSnvyDwFUpfbd2fSSwB0q7T1z7BNxVp5I5a7Gfn7RuvotDPAtV
a0tc7wH2NwOVm17nYYL1d812+l5g0ywOam4ug4knelaSBSeBTfZLZsnvgolb
Zyz0j2H/mEe/zgm/hYkkzXAtBRLYXA+/9okfMOHuMrz51QSw/4amutbIwISY
xy69Mfzevz9HWh8VAmdmeaCwXz1weGLWquZoAuftGeP1yjLAWXzp2a9oM+AE
XFpXdtkUOKK5Pdf2RAG7Qsq48bcEcNY3SzV8RF8RnHwicy0KOEr7vm147Q/M
3o3Oz7vxuXLX/eSKOWDejNproBAJHPWBHUeypIGpmBOtfywTODqEPdvJFBhq
1W81qhOBYy6Su5ooBVLuXPrKYHx+eMQt8fYlILrMslLEtgDH6ulGlrUXEFEK
lfcMB4Fjf6js5Ut5oH35WbZS8B5wPK62OV5LBmqKF+1Xmh1wzglyb+3whh/t
lPe6f8uB80DAVCpBEb7a9OcTnQeB82hIOGrnPHxJlDT5wYP1PnnQ+4P1GT5X
a3/J1d0PnPJ9zpX2afBJwtSwW7gCOC8Tg603L0B/U9rG3nfPgNPHl3+tZxi6
6OV1H28JA2egz/PXxVp4u/V93tIgKeB8KlRx1c+EjrB3ITkV2sAZMa7SuH8Q
Wnle5Tmg/3LIuM734fXwUuxX3VgEns+0uqatngW16ed6Pw3lAIejYJs3FgjV
YpwsfqlNwJlq+u5nrgwlK28PkTImwPmVVtTPyw/3pQXXkC5WwPnj5qNfPQp5
q9f+SK1dAZx/mlsKfV7C1dUTrnl1L4CzsDC9fG224ROvrQJm7Wv+B4S/r6E=

     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {0., 1.1309818079888752`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.571091776366897*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"-", 
    RowBox[{
     UnderoverscriptBox["\[Sum]", 
      RowBox[{"k", "=", "1"}], "100"], 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "k"], 
      FractionBox["2", 
       RowBox[{"k", " ", "\[Pi]"}]], 
      RowBox[{"Sin", "[", 
       RowBox[{"k", " ", "\[Pi]", " ", "x"}], "]"}]}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.473093991262122*^9, 3.473094036052011*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVVwc4Vt8f1y4ZGRFljx+ibZV8MzIrVBQhK6mISiUyMrIaksioJC0JFRll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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {0., 1.169034691153176}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.571091783800826*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"-", 
    RowBox[{
     UnderoverscriptBox["\[Sum]", 
      RowBox[{"k", "=", "1"}], "100"], 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "k"], 
      FractionBox["2", 
       RowBox[{"k", " ", "\[Pi]"}]], 
      RowBox[{"Sin", "[", 
       RowBox[{"k", " ", "\[Pi]", " ", "x"}], "]"}]}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.473122231679591*^9, 3.473122236653507*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwtW3k8lN/3R0hIUUkqShGSNm22U5GKokSppEKK6iMla5GlRCohoYhIlEoU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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-1.5, 1.5}, {-1.1684316327044206`, 1.1681927141889932`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.571091788952107*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowToolbars->"EditBar",
WindowSize->{795, 684},
WindowMargins->{{21, Automatic}, {Automatic, 23}},
PrintingCopies->1,
PrintingPageRange->{1, Automatic},
ShowSelection->True,
Magnification:>FEPrivate`If[
  FEPrivate`Equal[FEPrivate`$VersionNumber, 6.], 1.5, 1.5 Inherited],
FrontEndVersion->"7.0 for Mac OS X PowerPC (32-bit) (November 11, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 187, 2, 114, "Title"],
Cell[757, 26, 308, 7, 74, "Text"],
Cell[1068, 35, 443, 12, 114, "Text"],
Cell[1514, 49, 87, 1, 64, "Input"],
Cell[CellGroupData[{
Cell[1626, 54, 102, 1, 51, "Subsection"],
Cell[1731, 57, 450, 14, 62, "Text"],
Cell[2184, 73, 256, 9, 67, "Output"],
Cell[2443, 84, 249, 5, 62, "Text"],
Cell[CellGroupData[{
Cell[2717, 93, 820, 25, 128, "Input"],
Cell[3540, 120, 701, 20, 126, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4278, 145, 986, 30, 95, "Input"],
Cell[5267, 177, 41249, 690, 338, "Output"]
}, Open  ]],
Cell[46531, 870, 88, 1, 39, "Text"],
Cell[46622, 873, 339, 9, 71, "Input"],
Cell[CellGroupData[{
Cell[46986, 886, 1900, 65, 242, "Input"],
Cell[48889, 953, 169, 2, 40, "Output"],
Cell[49061, 957, 169, 2, 40, "Output"],
Cell[49233, 961, 169, 2, 40, "Output"],
Cell[49405, 965, 167, 2, 40, "Output"]
}, Open  ]],
Cell[49587, 970, 275, 8, 43, "Text"],
Cell[49865, 980, 218, 5, 44, "Output"],
Cell[50086, 987, 374, 7, 62, "Text"],
Cell[50463, 996, 87, 1, 64, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[50587, 1002, 157, 2, 51, "Subsection"],
Cell[50747, 1006, 176, 2, 39, "Text"],
Cell[50926, 1010, 389, 9, 49, "Input"],
Cell[51318, 1021, 163, 2, 39, "Text"],
Cell[CellGroupData[{
Cell[51506, 1027, 289, 8, 68, "Input"],
Cell[51798, 1037, 141, 2, 40, "Output"]
}, Open  ]],
Cell[51954, 1042, 168, 4, 39, "Text"],
Cell[CellGroupData[{
Cell[52147, 1050, 1170, 32, 107, "Input"],
Cell[53320, 1084, 11945, 209, 378, "Output"]
}, Open  ]],
Cell[65280, 1296, 395, 7, 62, "Text"],
Cell[CellGroupData[{
Cell[65700, 1307, 214, 6, 67, "Input"],
Cell[65917, 1315, 123, 2, 40, "Output"]
}, Open  ]],
Cell[66055, 1320, 298, 7, 84, "Text"],
Cell[CellGroupData[{
Cell[66378, 1331, 581, 17, 94, "Input"],
Cell[66962, 1350, 1753, 66, 538, "Output"]
}, Open  ]],
Cell[68730, 1419, 418, 8, 84, "Text"],
Cell[CellGroupData[{
Cell[69173, 1431, 1087, 28, 105, "Input"],
Cell[70263, 1461, 928, 26, 194, "Output"]
}, Open  ]],
Cell[71206, 1490, 181, 2, 39, "Text"],
Cell[71390, 1494, 380, 13, 80, "Input"],
Cell[71773, 1509, 234, 3, 39, "Text"],
Cell[CellGroupData[{
Cell[72032, 1516, 169, 5, 79, "Input"],
Cell[72204, 1523, 117, 2, 40, "Output"]
}, Open  ]],
Cell[72336, 1528, 185, 4, 62, "Text"],
Cell[CellGroupData[{
Cell[72546, 1536, 505, 17, 80, "Input"],
Cell[73054, 1555, 1125, 27, 286, "Output"]
}, Open  ]],
Cell[74194, 1585, 112, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[74331, 1590, 333, 10, 79, "Input"],
Cell[74667, 1602, 1154, 31, 129, "Output"]
}, Open  ]],
Cell[75836, 1636, 570, 14, 90, "Text"],
Cell[76409, 1652, 1120, 31, 160, "Input"],
Cell[CellGroupData[{
Cell[77554, 1687, 1090, 30, 157, "Input"],
Cell[78647, 1719, 12005, 206, 344, "Output"]
}, Open  ]],
Cell[90667, 1928, 368, 6, 62, "Text"],
Cell[CellGroupData[{
Cell[91060, 1938, 1225, 37, 164, "Input"],
Cell[92288, 1977, 11941, 204, 344, "Output"]
}, Open  ]],
Cell[104244, 2184, 165, 2, 39, "Text"],
Cell[CellGroupData[{
Cell[104434, 2190, 553, 17, 82, "Input"],
Cell[104990, 2209, 27733, 461, 327, "Output"]
}, Open  ]],
Cell[132738, 2673, 298, 6, 62, "Text"],
Cell[CellGroupData[{
Cell[133061, 2683, 689, 21, 125, "Input"],
Cell[133753, 2706, 42966, 710, 342, "Output"]
}, Open  ]],
Cell[176734, 3419, 87, 1, 64, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[176858, 3425, 114, 1, 51, "Subsection"],
Cell[176975, 3428, 129, 2, 39, "Text"],
Cell[177107, 3432, 256, 9, 67, "Output"],
Cell[177366, 3443, 98, 1, 39, "Text"],
Cell[177467, 3446, 234, 6, 44, "Output"],
Cell[177704, 3454, 97, 1, 39, "Text"],
Cell[177804, 3457, 225, 6, 71, "Input"],
Cell[178032, 3465, 88, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[178145, 3470, 353, 11, 72, "Input"],
Cell[178501, 3483, 326, 8, 67, "Output"]
}, Open  ]],
Cell[178842, 3494, 435, 14, 43, "Text"],
Cell[CellGroupData[{
Cell[179302, 3512, 256, 5, 44, "Input"],
Cell[179561, 3519, 144, 2, 40, "Output"]
}, Open  ]],
Cell[179720, 3524, 104, 1, 39, "Text"],
Cell[179827, 3527, 330, 9, 46, "Output"],
Cell[180160, 3538, 73, 1, 40, "Output"],
Cell[180236, 3541, 90, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[180351, 3546, 579, 16, 68, "Input"],
Cell[180933, 3564, 215, 5, 67, "Output"]
}, Open  ]],
Cell[181163, 3572, 358, 7, 62, "Text"],
Cell[CellGroupData[{
Cell[181546, 3583, 479, 14, 79, "Input"],
Cell[182028, 3599, 235, 5, 67, "Output"]
}, Open  ]],
Cell[182278, 3607, 131, 3, 39, "Text"],
Cell[CellGroupData[{
Cell[182434, 3614, 154, 2, 40, "Input"],
Cell[182591, 3618, 122, 2, 40, "Output"]
}, Open  ]],
Cell[182728, 3623, 350, 6, 62, "Text"],
Cell[CellGroupData[{
Cell[183103, 3633, 799, 24, 108, "Input"],
Cell[183905, 3659, 1974, 57, 434, "Output"]
}, Open  ]],
Cell[185894, 3719, 180, 4, 39, "Text"],
Cell[186077, 3725, 86, 1, 64, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[186200, 3731, 162, 3, 74, "Subsection"],
Cell[186365, 3736, 772, 24, 110, "Input"],
Cell[CellGroupData[{
Cell[187162, 3764, 632, 17, 64, "Input"],
Cell[187797, 3783, 4052, 74, 344, "Output"]
}, Open  ]],
Cell[191864, 3860, 816, 22, 87, "Input"],
Cell[192683, 3884, 295, 7, 62, "Text"],
Cell[192981, 3893, 1279, 35, 156, "Input"],
Cell[CellGroupData[{
Cell[194285, 3932, 344, 8, 40, "Input"],
Cell[194632, 3942, 21554, 377, 344, "Output"]
}, Open  ]],
Cell[216201, 4322, 579, 15, 129, "Text"],
Cell[216783, 4339, 1214, 35, 156, "Input"],
Cell[218000, 4376, 1155, 30, 87, "Input"],
Cell[CellGroupData[{
Cell[219180, 4410, 391, 9, 40, "Input"],
Cell[219574, 4421, 70981, 1173, 344, "Output"]
}, Open  ]],
Cell[290570, 5597, 389, 7, 84, "Text"],
Cell[290962, 5606, 1353, 35, 156, "Input"],
Cell[CellGroupData[{
Cell[292340, 5645, 550, 14, 64, "Input"],
Cell[292893, 5661, 2773, 51, 344, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[295703, 5717, 582, 14, 64, "Input"],
Cell[296288, 5733, 57002, 940, 351, "Output"]
}, Open  ]],
Cell[353305, 6676, 259, 5, 62, "Text"],
Cell[CellGroupData[{
Cell[353589, 6685, 585, 14, 64, "Input"],
Cell[354177, 6701, 142840, 2359, 359, 54542, 910, "CachedBoxData", "BoxData", \
"Output"]
}, Open  ]],
Cell[497032, 9063, 138, 3, 39, "Text"],
Cell[CellGroupData[{
Cell[497195, 9070, 635, 15, 64, "Input"],
Cell[497833, 9087, 57764, 952, 354, "Output"]
}, Open  ]],
Cell[555612, 10042, 495, 12, 62, "Text"],
Cell[556110, 10056, 410, 12, 68, "Output"],
Cell[556523, 10070, 123, 1, 39, "Text"],
Cell[556649, 10073, 206, 4, 62, "Text"],
Cell[CellGroupData[{
Cell[556880, 10081, 710, 21, 197, "Input"],
Cell[557593, 10104, 332, 10, 71, "Output"],
Cell[557928, 10116, 305, 9, 69, "Output"],
Cell[558236, 10127, 249, 7, 46, "Output"],
Cell[558488, 10136, 255, 6, 46, "Output"],
Cell[558746, 10144, 303, 8, 46, "Output"]
}, Open  ]],
Cell[559064, 10155, 509, 11, 87, "Text"],
Cell[559576, 10168, 94, 1, 40, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[559707, 10174, 119, 1, 51, "Subsection"],
Cell[CellGroupData[{
Cell[559851, 10179, 592, 16, 68, "Input"],
Cell[560446, 10197, 186, 3, 40, "Output"]
}, Open  ]],
Cell[560647, 10203, 583, 11, 107, "Text"],
Cell[CellGroupData[{
Cell[561255, 10218, 552, 15, 79, "Input"],
Cell[561810, 10235, 237, 5, 67, "Output"]
}, Open  ]],
Cell[562062, 10243, 95, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[562182, 10248, 606, 16, 79, "Input"],
Cell[562791, 10266, 289, 7, 69, "Output"]
}, Open  ]],
Cell[563095, 10276, 242, 9, 45, "Text"],
Cell[CellGroupData[{
Cell[563362, 10289, 194, 4, 40, "Input"],
Cell[563559, 10295, 239, 7, 69, "Output"]
}, Open  ]],
Cell[563813, 10305, 582, 9, 84, "Text"],
Cell[CellGroupData[{
Cell[564420, 10318, 767, 18, 82, "Input"],
Cell[565190, 10338, 251, 7, 69, "Output"]
}, Open  ]],
Cell[565456, 10348, 198, 4, 39, "Text"],
Cell[565657, 10354, 172, 4, 39, "Text"],
Cell[CellGroupData[{
Cell[565854, 10362, 260, 6, 40, "Input"],
Cell[566117, 10370, 232, 6, 40, "Output"]
}, Open  ]],
Cell[566364, 10379, 94, 1, 40, "Input"],
Cell[566461, 10382, 336, 8, 62, "Text"],
Cell[566800, 10392, 276, 8, 70, "Output"],
Cell[567079, 10402, 87, 1, 64, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[567203, 10408, 98, 1, 51, "Subsection"],
Cell[567304, 10411, 95, 1, 39, "Text"],
Cell[567402, 10414, 231, 5, 44, "Output"],
Cell[567636, 10421, 112, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[567773, 10426, 267, 5, 67, "Input"],
Cell[568043, 10433, 241, 6, 69, "Output"]
}, Open  ]],
Cell[568299, 10442, 189, 2, 39, "Text"],
Cell[CellGroupData[{
Cell[568513, 10448, 245, 5, 44, "Input"],
Cell[568761, 10455, 239, 7, 69, "Output"]
}, Open  ]],
Cell[569015, 10465, 146, 2, 87, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[569198, 10472, 179, 2, 51, "Subsection"],
Cell[569380, 10476, 104, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[569509, 10481, 236, 7, 44, "Input"],
Cell[569748, 10490, 72, 1, 40, "Output"]
}, Open  ]],
Cell[569835, 10494, 101, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[569961, 10499, 968, 29, 165, "Input"],
Cell[570932, 10530, 611, 20, 87, "Output"]
}, Open  ]],
Cell[571558, 10553, 159, 3, 39, "Text"],
Cell[CellGroupData[{
Cell[571742, 10560, 598, 19, 70, "Input"],
Cell[572343, 10581, 1068, 35, 164, "Output"]
}, Open  ]],
Cell[573426, 10619, 88, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[573539, 10624, 666, 22, 79, "Input"],
Cell[574208, 10648, 419, 11, 58, "Output"]
}, Open  ]],
Cell[574642, 10662, 119, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[574786, 10667, 159, 3, 44, "Input"],
Cell[574948, 10672, 280, 8, 67, "Output"]
}, Open  ]],
Cell[575243, 10683, 366, 10, 39, "Text"],
Cell[CellGroupData[{
Cell[575634, 10697, 498, 14, 56, "Input"],
Cell[576135, 10713, 495, 15, 79, "Output"]
}, Open  ]],
Cell[576645, 10731, 116, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[576786, 10736, 2380, 72, 286, "Input"],
Cell[579169, 10810, 901, 26, 84, "Output"],
Cell[580073, 10838, 580, 13, 55, "Output"]
}, Open  ]],
Cell[580668, 10854, 309, 5, 84, "Text"],
Cell[580980, 10861, 316, 10, 51, "Input"],
Cell[581299, 10873, 497, 8, 84, "Text"],
Cell[581799, 10883, 363, 12, 82, "Input"],
Cell[582165, 10897, 89, 1, 39, "Text"],
Cell[582257, 10900, 361, 11, 42, "Input"],
Cell[582621, 10913, 96, 1, 39, "Text"],
Cell[582720, 10916, 287, 7, 42, "Input"],
Cell[583010, 10925, 114, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[583149, 10930, 251, 5, 64, "Input"],
Cell[583403, 10937, 1104, 34, 164, "Output"],
Cell[584510, 10973, 1038, 31, 164, "Output"]
}, Open  ]],
Cell[585563, 11007, 210, 4, 39, "Text"],
Cell[585776, 11013, 519, 13, 65, "Input"],
Cell[CellGroupData[{
Cell[586320, 11030, 93, 2, 40, "Input"],
Cell[586416, 11034, 4146, 127, 500, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[590599, 11166, 129, 2, 40, "Input"],
Cell[590731, 11170, 2853, 81, 252, "Output"]
}, Open  ]],
Cell[593599, 11254, 3071, 85, 283, "Input"],
Cell[596673, 11341, 177, 4, 39, "Text"],
Cell[596853, 11347, 236, 5, 62, "Text"],
Cell[CellGroupData[{
Cell[597114, 11356, 148, 3, 44, "Input"],
Cell[597265, 11361, 247, 7, 44, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[597549, 11373, 1356, 30, 139, "Input"],
Cell[598908, 11405, 2681, 48, 504, "Output"]
}, Open  ]],
Cell[601604, 11456, 89, 1, 64, "Input"],
Cell[601696, 11459, 158, 3, 39, "Text"],
Cell[CellGroupData[{
Cell[601879, 11466, 124, 2, 40, "Input"],
Cell[602006, 11470, 184, 5, 46, "Output"]
}, Open  ]],
Cell[602205, 11478, 96, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[602326, 11483, 632, 19, 106, "Input"],
Cell[602961, 11504, 697, 23, 84, "Output"]
}, Open  ]],
Cell[603673, 11530, 90, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[603788, 11535, 525, 16, 55, "Input"],
Cell[604316, 11553, 417, 12, 50, "Output"]
}, Open  ]],
Cell[604748, 11568, 89, 1, 39, "Text"],
Cell[CellGroupData[{
Cell[604862, 11573, 712, 23, 91, "Input"],
Cell[605577, 11598, 357, 9, 46, "Output"]
}, Open  ]],
Cell[605949, 11610, 93, 1, 39, "Text"],
Cell[606045, 11613, 660, 19, 74, "Input"],
Cell[606708, 11634, 88, 1, 39, "Text"],
Cell[606799, 11637, 460, 12, 65, "Input"],
Cell[CellGroupData[{
Cell[607284, 11653, 162, 3, 40, "Input"],
Cell[607449, 11658, 409, 12, 44, "Output"]
}, Open  ]],
Cell[607873, 11673, 244, 8, 39, "Text"],
Cell[CellGroupData[{
Cell[608142, 11685, 206, 5, 68, "Input"],
Cell[608351, 11692, 215, 5, 44, "Output"]
}, Open  ]],
Cell[608581, 11700, 195, 6, 39, "Text"],
Cell[608779, 11708, 89, 1, 64, "Input"],
Cell[608871, 11711, 137, 4, 65, "Text"],
Cell[609011, 11717, 362, 7, 62, "Text"],
Cell[609376, 11726, 1031, 21, 377, "Text"],
Cell[610410, 11749, 352, 6, 84, "Text"],
Cell[610765, 11757, 313, 9, 40, "Output"],
Cell[611081, 11768, 576, 10, 129, "Text"],
Cell[CellGroupData[{
Cell[611682, 11782, 484, 13, 68, "Input"],
Cell[612169, 11797, 1896, 72, 199, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[614102, 11874, 374, 10, 81, "Input"],
Cell[614479, 11886, 2871, 90, 265, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[617387, 11981, 3483, 97, 329, "Input"],
Cell[620873, 12080, 34733, 577, 361, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[655643, 12662, 553, 17, 81, "Input"],
Cell[656199, 12681, 15510, 260, 361, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[671746, 12946, 578, 18, 81, "Input"],
Cell[672327, 12966, 21355, 356, 354, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)