(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 57341, 1102] NotebookOptionsPosition[ 56333, 1061] NotebookOutlinePosition[ 56676, 1076] CellTagsIndexPosition[ 56633, 1073] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Ac\[AAcute] defino el potencial correspondiente a una caja de largo, ancho y \ alto 1, con todas sus tapas a potencial cero excepto la tapa de arriba que \ est\[AAcute] a potencial 1. Elijo un sistema de coordenadas en la esquina de \ la caja. Dado que mi soluci\[OAcute]n es una doble serie, tengo un par\ \[AAcute]metro N, que me controla el l\[IAcute]mite superior de la suma. Dado \ que son dos sumas y ambas arrancan desde cero, para un dado N, la siguiente \ definicion suma (N+1)x(N+1) t\[EAcute]rminos. \ \>", "Subsection", CellChangeTimes->{{3.7452590095855727`*^9, 3.745259207147315*^9}, { 3.745259312298829*^9, 3.745259322537601*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", "y_", ",", "z_", ",", "N_"}], "]"}], ":=", RowBox[{"NSum", "[", RowBox[{ RowBox[{ FractionBox["16", SuperscriptBox["\[Pi]", "2"]], FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ")"}], "\[Pi]", " ", "x"}], "]"}], RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", "m"}], "+", "1"}], ")"}], "\[Pi]", " ", "y"}], "]"}]}], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"2", "m"}], "+", "1"}], ")"}]}]], FractionBox[ RowBox[{"Sinh", "[", RowBox[{"\[Pi]", " ", SqrtBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"2", "m"}], "+", "1"}], ")"}], "2"]}]], "z"}], "]"}], RowBox[{"Sinh", "[", RowBox[{"\[Pi]", " ", SqrtBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"2", "m"}], "+", "1"}], ")"}], "2"]}]]}], "]"}]]}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "N"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "N"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.7452576850089145`*^9, 3.7452578720452957`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Como se puede ver en los siguientes dos ejemplos, con N entre 4 y 5 sobra \ para tener una precisi\[OAcute]n de 7 d\[IAcute]gitos. Observar que los \ valores x, y, z los elijo entre 0 y 1. Esto se debe a que como mi caja tiene \ lado 1, el interior de la misma son valores entre 0 y 1. Observar que a \ medida que me acerco a alguna de las paredes, el N que necesito para obtener \ precisi\[OAcute]n aumenta.\ \>", "Subsection", CellChangeTimes->{{3.7452592134949064`*^9, 3.7452593875467854`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"0.2", ",", "0.3", ",", "0.5", ",", "N"}], "]"}], ",", RowBox[{"{", RowBox[{"N", ",", "0", ",", "20", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7452578778409157`*^9, 3.7452579164495544`*^9}, { 3.7452580469955745`*^9, 3.745258051353582*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{N$$ = 4, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[N$$], 0, 20, 1}}, Typeset`size$$ = {63., {0., 9.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, N$3197$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {N$$ = 0}, "ControllerVariables" :> { Hold[N$$, N$3197$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`f[0.2, 0.3, 0.5, N$$], "Specifications" :> {{N$$, 0, 20, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{257., {64., 69.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.745257898186434*^9, 3.745257918841777*^9}, 3.745258052109432*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"0.8", ",", "0.33", ",", "0.18", ",", "N"}], "]"}], ",", RowBox[{"{", RowBox[{"N", ",", "0", ",", "20", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7452581340527377`*^9, 3.7452581483229027`*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{N$$ = 5, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[N$$], 0, 20, 1}}, Typeset`size$$ = {63., {0., 9.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, N$3222$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {N$$ = 0}, "ControllerVariables" :> { Hold[N$$, N$3222$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`f[0.8, 0.33, 0.18, N$$], "Specifications" :> {{N$$, 0, 20, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{257., {64., 69.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.7452581493533072`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ac\[AAcute] ploteo para valores de y, z fijos, moviendome en x. Como es de \ esperar el potencial va de 0 a 0. La l\[IAcute]nea m\[AAcute]s alta y la m\ \[AAcute]s baja son las m\[AAcute]s cercanas a la pared y por lo tanto las \ que requieren m\[AAcute]s precisi\[OAcute]n.\ \>", "Subsection", CellChangeTimes->{{3.745259411150917*^9, 3.745259505804691*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f", "[", RowBox[{"x", ",", "0.1", ",", "0.1", ",", "4"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"x", ",", "0.3", ",", "0.3", ",", "4"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"x", ",", "0.5", ",", "0.5", ",", "4"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"x", ",", "0.7", ",", "0.7", ",", "4"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"x", ",", "0.9", ",", "0.9", ",", "6"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.745258185903738*^9, 3.745258229564367*^9}, { 3.745258265442567*^9, 3.7452583771151695`*^9}, {3.7452584754221163`*^9, 3.7452584759553585`*^9}}], Cell[BoxData[ 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