(* Content-type: application/vnd.wolfram.mathematica *)

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

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[      7650,        187]
NotebookOptionsPosition[      7138,        170]
NotebookOutlinePosition[      7474,        185]
CellTagsIndexPosition[      7431,        182]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[{
 RowBox[{
  RowBox[{"\[HBar]", "=", "1"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Psi]", "[", 
    RowBox[{"x_", ",", "t_", ",", "k_", ",", "m_", ",", "\[Sigma]_"}], "]"}], 
   ":=", 
   RowBox[{
    FractionBox["1", 
     SuperscriptBox["\[Pi]", 
      FractionBox["1", "4"]]], 
    SqrtBox[
     FractionBox[
      RowBox[{"m", " ", "\[Sigma]"}], 
      RowBox[{"m", "+", 
       RowBox[{"\[ImaginaryI]", " ", "\[HBar]", " ", 
        SuperscriptBox["\[Sigma]", "2"], "t", " "}]}]]], 
    RowBox[{"Exp", "[", 
     FractionBox[
      RowBox[{
       RowBox[{"2", "m", " ", "k", " ", "x"}], "+", 
       RowBox[{"\[ImaginaryI]", " ", "m", " ", 
        SuperscriptBox["\[Sigma]", "2"], 
        SuperscriptBox["x", "2"]}], "-", 
       RowBox[{"\[HBar]", " ", 
        SuperscriptBox["k", "2"], "t"}]}], 
      RowBox[{
       RowBox[{"2", 
        SuperscriptBox["\[Sigma]", "2"], "\[HBar]", " ", "t"}], "-", 
       RowBox[{"2", "\[ImaginaryI]", " ", "m"}]}]], "]"}]}]}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.794578252294245*^9, 3.794578452959436*^9}, {
   3.7945785370165043`*^9, 3.79457853748568*^9}, {3.794616755960895*^9, 
   3.794616759775206*^9}, 3.794616848094949*^9, {3.794616988272946*^9, 
   3.7946170067124243`*^9}, {3.7946171716320457`*^9, 3.794617171924404*^9}, {
   3.794617248485178*^9, 3.794617248810408*^9}, {3.794617289811347*^9, 
   3.794617292704303*^9}, {3.794617536916334*^9, 3.794617547297842*^9}, {
   3.794617802037415*^9, 3.7946178047867537`*^9}, {3.794618814580202*^9, 
   3.794618821784058*^9}},
 CellLabel->
  "In[137]:=",ExpressionUUID->"7260f8ac-8450-4836-8588-6fc6af9fb5ac"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Manipulate", "[", 
   RowBox[{
    RowBox[{"Plot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"\[Psi]", "[", 
        RowBox[{"x", ",", "t", ",", "k", ",", "m", ",", "\[Sigma]"}], "]"}], 
       RowBox[{
        RowBox[{"\[Psi]", "[", 
         RowBox[{"x", ",", "t", ",", "k", ",", "m", ",", "\[Sigma]"}], "]"}], 
        "\[Conjugate]"}]}], ",", 
      RowBox[{"{", 
       RowBox[{"x", ",", 
        RowBox[{"-", "30"}], ",", "30"}], "}"}], ",", 
      RowBox[{"PlotRange", "\[Rule]", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"-", "30"}], ",", "30"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"0", ",", "0.6"}], "}"}]}], "}"}]}]}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "1", ",", "100"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"k", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"m", ",", "1", ",", "10"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"\[Sigma]", ",", "1", ",", "5"}], "}"}]}], "]"}], 
  "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.7946164530549726`*^9, 3.794616688352764*^9}, {
   3.794616736209124*^9, 3.794616751236594*^9}, {3.794616835398952*^9, 
   3.794617052207549*^9}, {3.794617088251671*^9, 3.794617091887043*^9}, {
   3.794617156894855*^9, 3.7946171787317133`*^9}, {3.794617209149869*^9, 
   3.794617262211957*^9}, 3.794617314059188*^9, {3.794617403504603*^9, 
   3.794617404534224*^9}, {3.794617459791314*^9, 3.794617504562406*^9}, {
   3.794617554962022*^9, 3.794617653462476*^9}, {3.7946176857056847`*^9, 
   3.7946177160496063`*^9}, {3.794617754412051*^9, 3.7946178291618853`*^9}, {
   3.794617864043325*^9, 3.79461787077711*^9}, {3.794618160172831*^9, 
   3.794618191488502*^9}, {3.794618275113809*^9, 3.794618300613534*^9}, 
   3.7946183727670937`*^9, {3.794618422942705*^9, 3.79461843835427*^9}, {
   3.7946186375998793`*^9, 3.7946187466580772`*^9}, {3.7946188254273252`*^9, 
   3.79461882985839*^9}, {3.7946188617776413`*^9, 3.794618882414401*^9}},
 CellLabel->
  "In[141]:=",ExpressionUUID->"31ab1382-6989-406f-a631-1f4e354ef706"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`k$$ = -1, $CellContext`m$$ = 
    2., $CellContext`t$$ = 1., $CellContext`\[Sigma]$$ = 1, Typeset`show$$ = 
    True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`t$$], 1, 100}, {
      Hold[$CellContext`k$$], -1, 1}, {
      Hold[$CellContext`m$$], 1, 10}, {
      Hold[$CellContext`\[Sigma]$$], 1, 5}}, Typeset`size$$ = {
    360., {116., 121.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`t$472910$$ = 
    0, $CellContext`k$472911$$ = 0, $CellContext`m$472912$$ = 
    0, $CellContext`\[Sigma]$472913$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`k$$ = -1, $CellContext`m$$ = 
        1, $CellContext`t$$ = 1, $CellContext`\[Sigma]$$ = 1}, 
      "ControllerVariables" :> {
        Hold[$CellContext`t$$, $CellContext`t$472910$$, 0], 
        Hold[$CellContext`k$$, $CellContext`k$472911$$, 0], 
        Hold[$CellContext`m$$, $CellContext`m$472912$$, 0], 
        Hold[$CellContext`\[Sigma]$$, $CellContext`\[Sigma]$472913$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, 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, $CellContext`t$$, \
$CellContext`k$$, $CellContext`m$$, $CellContext`\[Sigma]$$] Conjugate[
          $CellContext`\[Psi][$CellContext`x, $CellContext`t$$, \
$CellContext`k$$, $CellContext`m$$, $CellContext`\[Sigma]$$]], \
{$CellContext`x, -30, 30}, PlotRange -> {{-30, 30}, {0, 0.6}}], 
      "Specifications" :> {{$CellContext`t$$, 1, 100}, {$CellContext`k$$, -1, 
         1}, {$CellContext`m$$, 1, 10}, {$CellContext`\[Sigma]$$, 1, 5}}, 
      "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{405., {230., 236.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{{3.794618661720572*^9, 3.7946187842566767`*^9}, {
  3.794618830359417*^9, 3.7946188923367023`*^9}},
 CellLabel->
  "Out[141]=",ExpressionUUID->"e97d6366-4332-4bbe-82aa-f4d2de3b65af"]
}, Open  ]]
},
WindowSize->{1280, 702},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"12.0 for Mac OS X x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 1657, 41, 96, "Input",ExpressionUUID->"7260f8ac-8450-4836-8588-6fc6af9fb5ac"],
Cell[CellGroupData[{
Cell[2240, 65, 2158, 48, 67, "Input",ExpressionUUID->"31ab1382-6989-406f-a631-1f4e354ef706"],
Cell[4401, 115, 2721, 52, 519, "Output",ExpressionUUID->"e97d6366-4332-4bbe-82aa-f4d2de3b65af"]
}, Open  ]]
}
]
*)