Problem Set 3 - ( (* Content-type: application/mathematica...

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(* Content-type: application/mathematica *) ( (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) ( (* CreatedBy='Mathematica 6.0' *) ( (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 11033, 351] NotebookOptionsPosition[ 9674, 303] NotebookOutlinePosition[ 10341, 325] CellTagsIndexPosition[ 10298, 322] WindowFrame->Normal ContainsDynamic->False*) C (* Beginning of Notebook Content *) Notebook[{ N Cell[CellGroupData[{ Cell["Problem Set 3", "Title", CellChangeTimes->{{3.4313993853859997`*^9, 3.431399390368*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input", CellChangeTimes->{{3.4314006017799997`*^9, 3.431400619302*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"$Assumptions", "=", RowBox[{"{", RowBox[{"A", "\[Element]", "Reals"}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.431400571337*^9, 3.431400623844*^9}}], Cell["1. Discontinuous Wavefunctions", "Section", CellChangeTimes->{{3.43139939969*^9, 3.43139940873*^9}}], Cell[CellGroupData[{ C Cell["(a)", "Section", CellChangeTimes->{{3.43139982583*^9, 3.431399826691*^9}}], Cell[CellGroupData[{ C Cell[BoxData[ RowBox[{ StyleBox["\[CapitalPsi]", FontSize->24], StyleBox["=", FontSize->24], RowBox[{ StyleBox["\[Piecewise]", FontSize->24], GridBox[{ { RowBox[{ RowBox[{
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StyleBox[ RowBox[{ StyleBox["A", FontSize->24], "Sin"}]], "[", FractionBox[ RowBox[{"\[Pi]", " ", "x"}], "2"], "]"}], SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "5"}], RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}]]}], RowBox[{"0", "\[LessEqual]", "x", "\[LessEqual]", "1"}]}, { RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", FractionBox[ RowBox[{"\[Pi]", " ", "x"}], "2"], "]"}]}], SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "5"}], RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}]}]]}], RowBox[{"1", "<", "x", "\[LessEqual]", "2"}]} }]}]}]], "Input", CellChangeTimes->{{3.431399455074*^9, 3.431399472376*^9}, {3.431399578553*^9, 3.4313997873859997`*^9}, {3.431401646642*^9, 3.431401678785*^9}}, FontSize->36], Cell[BoxData[ RowBox[{"\[Piecewise]", GridBox[{ { RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "5"}], " ", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}]], " ", RowBox[{"ASin", "[", FractionBox[ RowBox[{"\[Pi]", " ", "x"}], "2"], "]"}]}], RowBox[{"0", "\[LessEqual]", "x", "\[LessEqual]", "1"}]}, { RowBox[{ RowBox[{"-", SuperscriptBox["\[ExponentialE]",
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Problem Set 3 - ( (* Content-type: application/mathematica...

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