trunk/multipole/CDTensor.nb

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

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

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     18049,        524]
NotebookOptionsPosition[     17236,        490]
NotebookOutlinePosition[     17591,        506]
CellTagsIndexPosition[     17548,        503]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[{
 RowBox[{
  RowBox[{"rc", "=."}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Kappa]", "=."}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ", 
   RowBox[{
    RowBox[{"Erfc", "[", 
     RowBox[{"\[Kappa]", " ", "r"}], "]"}], "/", "r"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"g", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "2"}], "*", "\[Kappa]"}], ")"}], "/", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"E", "^", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"r", "^", "2"}], "*", 
          RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*", 
       RowBox[{"Sqrt", "[", "Pi", "]"}], "*", "r"}], ")"}]}], "-", 
    RowBox[{
     RowBox[{"Erfc", "[", 
      RowBox[{"r", "*", "\[Kappa]"}], "]"}], "/", 
     RowBox[{"r", "^", "2"}]}]}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"h", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"4", "*", "\[Kappa]"}], ")"}], "/", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"E", "^", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"r", "^", "2"}], "*", 
          RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*", 
       RowBox[{"Sqrt", "[", "Pi", "]"}], "*", 
       RowBox[{"r", "^", "2"}]}], ")"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"4", "*", 
       RowBox[{"\[Kappa]", "^", "3"}]}], ")"}], "/", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"E", "^", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"r", "^", "2"}], "*", 
          RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*", 
       RowBox[{"Sqrt", "[", "Pi", "]"}]}], ")"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "*", 
       RowBox[{"Erfc", "[", 
        RowBox[{"r", "*", "\[Kappa]"}], "]"}]}], ")"}], "/", 
     RowBox[{"r", "^", "3"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"f1", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ", 
   RowBox[{
    RowBox[{"f", "[", 
     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ", 
    RowBox[{"f", "[", 
     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"r", "-", "rc"}], ")"}], 
     RowBox[{"g", "[", 
      RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], "-", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"r", "-", "rc"}], ")"}], "^", "2"}], " ", 
     RowBox[{
      RowBox[{"h", "[", 
       RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "2"}]}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"g1", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ", 
   RowBox[{
    RowBox[{"g", "[", 
     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ", 
    RowBox[{"g", "[", 
     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"r", "-", "rc"}], ")"}], 
     RowBox[{"h", "[", 
      RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"h1", "[", 
    RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"h", "[", 
     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", 
    RowBox[{"h", "[", 
     RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"v11", "[", 
    RowBox[{"r_", ",", "method_"}], "]"}], ":=", 
   RowBox[{"Switch", "[", 
    RowBox[{"method", ",", "\[IndentingNewLine]", "BARE", ",", " ", 
     RowBox[{"g", "[", 
      RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]", 
     "TSF", ",", " ", 
     RowBox[{"g1", "[", 
      RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", "\[IndentingNewLine]", "SP",
      ",", " ", 
     RowBox[{
      RowBox[{"g", "[", 
       RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ", 
      RowBox[{"g", "[", 
       RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], ",", "\[IndentingNewLine]", 
     "GSF", ",", " ", 
     RowBox[{
      RowBox[{"g", "[", 
       RowBox[{"r", ",", "\[Kappa]"}], "]"}], " ", "-", " ", 
      RowBox[{"g", "[", 
       RowBox[{"rc", ",", "\[Kappa]"}], "]"}], " ", "-", " ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"r", "-", "rc"}], ")"}], 
       RowBox[{"h", "[", 
        RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}]}], "\[IndentingNewLine]", 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"v11prime", "[", 
    RowBox[{"r_", ",", " ", "method_"}], "]"}], ":=", " ", 
   RowBox[{"Switch", "[", 
    RowBox[{"method", ",", " ", "\[IndentingNewLine]", "BARE", ",", 
     RowBox[{"h", "[", 
      RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]", 
     "TSF", ",", " ", 
     RowBox[{"h1", "[", 
      RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]", 
     "SP", ",", " ", 
     RowBox[{"h", "[", 
      RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]", 
     "GSF", ",", " ", 
     RowBox[{
      RowBox[{"h", "[", 
       RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", 
      RowBox[{"h", "[", 
       RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}], "\[IndentingNewLine]", 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"R", "[", "\[Alpha]_", "]"}], " ", ":=", 
   RowBox[{"r", " ", 
    RowBox[{"Switch", "[", 
     RowBox[{"\[Alpha]", ",", " ", "\[IndentingNewLine]", "1", ",", 
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], 
       RowBox[{"Cos", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
       "2", ",", 
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
       "3", ",", 
      RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"T", "[", 
    RowBox[{"\[Alpha]_", ",", "\[Beta]_", ",", " ", "method_"}], "]"}], " ", ":=",
    " ", 
   RowBox[{
    RowBox[{
     RowBox[{"KroneckerDelta", "[", 
      RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "*", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"v11", "[", 
        RowBox[{"r", ",", "method"}], "]"}], "/", "r"}], ")"}]}], "+", " ", 
    RowBox[{
     RowBox[{"R", "[", "\[Alpha]", "]"}], 
     RowBox[{"R", "[", "\[Beta]", "]"}], 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"v11prime", "[", 
         RowBox[{"r", ",", "method"}], "]"}], "-", 
        RowBox[{
         RowBox[{"v11", "[", 
          RowBox[{"r", ",", "method"}], "]"}], "/", "r"}]}], ")"}], "/", 
      RowBox[{"r", "^", "2"}]}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TBare", " ", "=", " ", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"Integrate", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"r", "^", "2"}], 
           RowBox[{"Integrate", "[", 
            RowBox[{
             RowBox[{"Integrate", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"Sin", "[", "\[Theta]", "]"}], 
                RowBox[{"T", "[", 
                 RowBox[{"i", ",", "j", ",", "BARE"}], "]"}]}], ",", 
               RowBox[{"{", 
                RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}], 
             ",", 
             RowBox[{"{", 
              RowBox[{"\[Phi]", ",", "0", ",", 
               RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TSP", " ", "=", " ", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"Integrate", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"r", "^", "2"}], 
           RowBox[{"Integrate", "[", 
            RowBox[{
             RowBox[{"Integrate", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"Sin", "[", "\[Theta]", "]"}], 
                RowBox[{"T", "[", 
                 RowBox[{"i", ",", "j", ",", "SP"}], "]"}]}], ",", 
               RowBox[{"{", 
                RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}], 
             ",", 
             RowBox[{"{", 
              RowBox[{"\[Phi]", ",", "0", ",", 
               RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TGSF", " ", "=", " ", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"Integrate", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"r", "^", "2"}], 
           RowBox[{"Integrate", "[", 
            RowBox[{
             RowBox[{"Integrate", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"Sin", "[", "\[Theta]", "]"}], 
                RowBox[{"T", "[", 
                 RowBox[{"i", ",", "j", ",", "GSF"}], "]"}]}], ",", 
               RowBox[{"{", 
                RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}], 
             ",", 
             RowBox[{"{", 
              RowBox[{"\[Phi]", ",", "0", ",", 
               RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TTSF", " ", "=", " ", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"Integrate", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"r", "^", "2"}], 
           RowBox[{"Integrate", "[", 
            RowBox[{
             RowBox[{"Integrate", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"Sin", "[", "\[Theta]", "]"}], 
                RowBox[{"T", "[", 
                 RowBox[{"i", ",", "j", ",", "TSF"}], "]"}]}], ",", 
               RowBox[{"{", 
                RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}], 
             ",", 
             RowBox[{"{", 
              RowBox[{"\[Phi]", ",", "0", ",", 
               RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"QBARE", " ", "=", 
   RowBox[{"3", 
    RowBox[{
     RowBox[{"Part", "[", 
      RowBox[{"TBare", ",", "1", ",", "1", ",", "1"}], "]"}], "/", 
     RowBox[{"(", 
      RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"QTSP", " ", "=", " ", 
   RowBox[{"3", 
    RowBox[{
     RowBox[{"Part", "[", 
      RowBox[{"TSP", ",", "1", ",", "1", ",", "1"}], "]"}], "/", 
     RowBox[{"(", 
      RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"QGSF", " ", "=", "  ", 
   RowBox[{"3", 
    RowBox[{
     RowBox[{"Part", "[", 
      RowBox[{"TGSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/", 
     RowBox[{"(", 
      RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"QTSF", " ", "=", " ", 
   RowBox[{"3", 
    RowBox[{
     RowBox[{"Part", "[", 
      RowBox[{"TTSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/", 
     RowBox[{"(", 
      RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.613731558054296*^9, 3.613732200209785*^9}, 
   3.6137322781282454`*^9, {3.61373233169027*^9, 3.613732397354877*^9}, {
   3.613732488348338*^9, 3.6137327713906393`*^9}, {3.613732810835518*^9, 
   3.613732821957967*^9}, {3.613732862763562*^9, 3.613732913141625*^9}, {
   3.61373295595298*^9, 3.613733106904414*^9}, {3.613733177027177*^9, 
   3.613733199740512*^9}, {3.61373326352699*^9, 3.6137332727080936`*^9}, {
   3.613733425731758*^9, 3.6137335719815893`*^9}, {3.613733605778666*^9, 
   3.613733648768111*^9}, {3.613733776819376*^9, 3.6137338150569887`*^9}, {
   3.6137338699918118`*^9, 3.61373393057332*^9}, {3.613733985426153*^9, 
   3.613733985628289*^9}, {3.613734054134171*^9, 3.6137340588514023`*^9}, {
   3.6137371511302147`*^9, 3.613737188118826*^9}, {3.613815304031159*^9, 
   3.613815306899302*^9}, {3.613815415274508*^9, 3.613815450160325*^9}, {
   3.613815535717202*^9, 3.613815604127789*^9}, {3.613815665097225*^9, 
   3.613815673383039*^9}, {3.613816023942026*^9, 3.6138160527230864`*^9}, {
   3.613825536655637*^9, 3.613825555245915*^9}, {3.613825660601698*^9, 
   3.6138256692518787`*^9}, {3.613825968874196*^9, 3.613826000721004*^9}, {
   3.6138263115515537`*^9, 3.613826312408416*^9}, {3.613826919678602*^9, 
   3.613826920319913*^9}, {3.613827178556149*^9, 3.6138272197490597`*^9}, {
   3.6138410090125504`*^9, 3.613841090576209*^9}, {3.613841142597171*^9, 
   3.613841191624243*^9}, {3.6138412274048777`*^9, 3.613841229484283*^9}, {
   3.6138413897003736`*^9, 3.613841438224633*^9}, {3.61384150925097*^9, 
   3.6138415133903227`*^9}, {3.613841547354535*^9, 3.613841573983226*^9}, {
   3.613898318732862*^9, 3.613898326606717*^9}, {3.614440844373805*^9, 
   3.614440869838758*^9}, {3.61444103194166*^9, 3.614441084299322*^9}, {
   3.614441116069621*^9, 3.614441164401059*^9}, {3.6144412214281187`*^9, 
   3.614441279916031*^9}, {3.6144413160863132`*^9, 3.614441341635235*^9}, {
   3.614441394376206*^9, 3.614441421059911*^9}, {3.6144416231023483`*^9, 
   3.614441625159938*^9}, {3.614442650450296*^9, 3.6144427006914186`*^9}, {
   3.614442735072257*^9, 3.614442776902771*^9}, {3.614442819684997*^9, 
   3.614442867826069*^9}, {3.614442914658215*^9, 3.614442924512073*^9}}],

Cell[CellGroupData[{

Cell[BoxData["QBARE"], "Input",
 CellChangeTimes->{{3.61389845863691*^9, 3.6138984602794447`*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"3", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox["8", "3"]}], " ", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{
        RowBox[{"-", 
         SuperscriptBox["rc", "2"]}], " ", 
        SuperscriptBox["\[Kappa]", "2"]}]], " ", 
      SqrtBox["\[Pi]"], " ", "rc", " ", "\[Kappa]"}], "+", 
     RowBox[{
      FractionBox["4", "3"], " ", "\[Pi]", " ", 
      RowBox[{"Erf", "[", 
       RowBox[{"rc", " ", "\[Kappa]"}], "]"}]}]}], ")"}]}], 
  RowBox[{"4", " ", "\[Pi]"}]]], "Output",
 CellChangeTimes->{
  3.61389846058971*^9, {3.6144418380848494`*^9, 3.614441838682383*^9}, {
   3.614443124832337*^9, 3.614443142122366*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["QTSP"], "Input",
 CellChangeTimes->{{3.613898461774685*^9, 3.61389846255107*^9}}],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{3.6138984628297167`*^9, 3.614441838710091*^9, 
  3.614443128936681*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"QGSF", " "}]], "Input",
 CellChangeTimes->{{3.613898464699469*^9, 3.613898465498917*^9}, {
   3.614441850430952*^9, 3.6144418663262777`*^9}, 3.61444313552145*^9}],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{
  3.613898465771669*^9, {3.614441838760746*^9, 3.614441866820423*^9}, {
   3.614443131316518*^9, 3.614443135852601*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["QTSF"], "Input",
 CellChangeTimes->{{3.613898466555105*^9, 3.613898468075191*^9}}],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{3.613898468428026*^9, 3.614441838800758*^9, 
  3.614443138734713*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FullSimplify", "[", "QTSP", "]"}]], "Input",
 CellChangeTimes->{{3.613898477301433*^9, 3.613898481802129*^9}}],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{3.613898482310692*^9, 3.614441838849948*^9}]
}, Open  ]]
},
WindowSize->{884, 1337},
WindowMargins->{{500, Automatic}, {Automatic, 0}},
FrontEndVersion->"10.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 27, \
2014)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 14650, 396, 811, "Input"],
Cell[CellGroupData[{
Cell[15232, 420, 98, 1, 28, "Input"],
Cell[15333, 423, 719, 21, 58, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16089, 449, 95, 1, 28, "Input"],
Cell[16187, 452, 119, 2, 28, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16343, 459, 186, 3, 28, "Input"],
Cell[16532, 464, 169, 3, 28, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16738, 472, 96, 1, 28, "Input"],
Cell[16837, 475, 117, 2, 28, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16991, 482, 134, 2, 28, "Input"],
Cell[17128, 486, 92, 1, 28, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
Revision:	4195
Committed:	Thu Jul 17 18:24:41 2014 UTC (9 years, 11 months ago) by gezelter
File size:	18247 byte(s)
Log Message:	Most recent version including dielectric stuff
#	User	Rev	Content
1	gezelter	4195	(* Content-type: application/vnd.wolfram.mathematica *)
2
3			(* Wolfram Notebook File *)
4			(* http://www.wolfram.com/nb *)
5
6			(* CreatedBy='Mathematica 9.0' *)
7
8			(CacheID: 234)
9			(* Internal cache information:
10			NotebookFileLineBreakTest
11			NotebookFileLineBreakTest
12			NotebookDataPosition[ 157, 7]
13			NotebookDataLength[ 18049, 524]
14			NotebookOptionsPosition[ 17236, 490]
15			NotebookOutlinePosition[ 17591, 506]
16			CellTagsIndexPosition[ 17548, 503]
17			WindowFrame->Normal*)
18
19			(* Beginning of Notebook Content *)
20			Notebook[{
21			Cell[BoxData[{
22			RowBox[{
23			RowBox[{"rc", "=."}], ";"}], "\[IndentingNewLine]",
24			RowBox[{
25			RowBox[{"\[Kappa]", "=."}], ";"}], "\[IndentingNewLine]",
26			RowBox[{
27			RowBox[{
28			RowBox[{"f", "[",
29			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
30			RowBox[{
31			RowBox[{"Erfc", "[",
32			RowBox[{"\[Kappa]", " ", "r"}], "]"}], "/", "r"}]}],
33			";"}], "\[IndentingNewLine]",
34			RowBox[{
35			RowBox[{
36			RowBox[{"g", "[",
37			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
38			RowBox[{
39			RowBox[{
40			RowBox[{"(",
41			RowBox[{
42			RowBox[{"-", "2"}], "*", "\[Kappa]"}], ")"}], "/",
43			RowBox[{"(",
44			RowBox[{
45			RowBox[{"E", "^",
46			RowBox[{"(",
47			RowBox[{
48			RowBox[{"r", "^", "2"}], "*",
49			RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
50			RowBox[{"Sqrt", "[", "Pi", "]"}], "*", "r"}], ")"}]}], "-",
51			RowBox[{
52			RowBox[{"Erfc", "[",
53			RowBox[{"r", "*", "\[Kappa]"}], "]"}], "/",
54			RowBox[{"r", "^", "2"}]}]}]}], " ", ";"}], "\[IndentingNewLine]",
55			RowBox[{
56			RowBox[{
57			RowBox[{"h", "[",
58			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=",
59			RowBox[{
60			RowBox[{
61			RowBox[{"(",
62			RowBox[{"4", "*", "\[Kappa]"}], ")"}], "/",
63			RowBox[{"(",
64			RowBox[{
65			RowBox[{"E", "^",
66			RowBox[{"(",
67			RowBox[{
68			RowBox[{"r", "^", "2"}], "*",
69			RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
70			RowBox[{"Sqrt", "[", "Pi", "]"}], "*",
71			RowBox[{"r", "^", "2"}]}], ")"}]}], "+",
72			RowBox[{
73			RowBox[{"(",
74			RowBox[{"4", "*",
75			RowBox[{"\[Kappa]", "^", "3"}]}], ")"}], "/",
76			RowBox[{"(",
77			RowBox[{
78			RowBox[{"E", "^",
79			RowBox[{"(",
80			RowBox[{
81			RowBox[{"r", "^", "2"}], "*",
82			RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
83			RowBox[{"Sqrt", "[", "Pi", "]"}]}], ")"}]}], "+",
84			RowBox[{
85			RowBox[{"(",
86			RowBox[{"2", "*",
87			RowBox[{"Erfc", "[",
88			RowBox[{"r", "*", "\[Kappa]"}], "]"}]}], ")"}], "/",
89			RowBox[{"r", "^", "3"}]}]}]}], ";"}], "\[IndentingNewLine]",
90			RowBox[{
91			RowBox[{
92			RowBox[{"f1", "[",
93			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
94			RowBox[{
95			RowBox[{"f", "[",
96			RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ",
97			RowBox[{"f", "[",
98			RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
99			RowBox[{
100			RowBox[{"(",
101			RowBox[{"r", "-", "rc"}], ")"}],
102			RowBox[{"g", "[",
103			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], "-",
104			RowBox[{
105			RowBox[{
106			RowBox[{"(",
107			RowBox[{"r", "-", "rc"}], ")"}], "^", "2"}], " ",
108			RowBox[{
109			RowBox[{"h", "[",
110			RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "2"}]}]}]}], " ",
111			";"}], "\[IndentingNewLine]",
112			RowBox[{
113			RowBox[{
114			RowBox[{"g1", "[",
115			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
116			RowBox[{
117			RowBox[{"g", "[",
118			RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ",
119			RowBox[{"g", "[",
120			RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
121			RowBox[{
122			RowBox[{"(",
123			RowBox[{"r", "-", "rc"}], ")"}],
124			RowBox[{"h", "[",
125			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}]}],
126			";"}], "\[IndentingNewLine]",
127			RowBox[{
128			RowBox[{
129			RowBox[{"h1", "[",
130			RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=",
131			RowBox[{
132			RowBox[{"h", "[",
133			RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
134			RowBox[{"h", "[",
135			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}], " ",
136			";"}], "\[IndentingNewLine]",
137			RowBox[{
138			RowBox[{
139			RowBox[{"v11", "[",
140			RowBox[{"r_", ",", "method_"}], "]"}], ":=",
141			RowBox[{"Switch", "[",
142			RowBox[{"method", ",", "\[IndentingNewLine]", "BARE", ",", " ",
143			RowBox[{"g", "[",
144			RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]",
145			"TSF", ",", " ",
146			RowBox[{"g1", "[",
147			RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", "\[IndentingNewLine]", "SP",
148			",", " ",
149			RowBox[{
150			RowBox[{"g", "[",
151			RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ",
152			RowBox[{"g", "[",
153			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], ",", "\[IndentingNewLine]",
154			"GSF", ",", " ",
155			RowBox[{
156			RowBox[{"g", "[",
157			RowBox[{"r", ",", "\[Kappa]"}], "]"}], " ", "-", " ",
158			RowBox[{"g", "[",
159			RowBox[{"rc", ",", "\[Kappa]"}], "]"}], " ", "-", " ",
160			RowBox[{
161			RowBox[{"(",
162			RowBox[{"r", "-", "rc"}], ")"}],
163			RowBox[{"h", "[",
164			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}]}], "\[IndentingNewLine]",
165			"]"}]}], ";"}], "\[IndentingNewLine]",
166			RowBox[{
167			RowBox[{
168			RowBox[{"v11prime", "[",
169			RowBox[{"r_", ",", " ", "method_"}], "]"}], ":=", " ",
170			RowBox[{"Switch", "[",
171			RowBox[{"method", ",", " ", "\[IndentingNewLine]", "BARE", ",",
172			RowBox[{"h", "[",
173			RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]",
174			"TSF", ",", " ",
175			RowBox[{"h1", "[",
176			RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]",
177			"SP", ",", " ",
178			RowBox[{"h", "[",
179			RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",", " ", "\[IndentingNewLine]",
180			"GSF", ",", " ",
181			RowBox[{
182			RowBox[{"h", "[",
183			RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
184			RowBox[{"h", "[",
185			RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}], "\[IndentingNewLine]",
186			"]"}]}], ";"}], "\[IndentingNewLine]",
187			RowBox[{
188			RowBox[{
189			RowBox[{"R", "[", "\[Alpha]_", "]"}], " ", ":=",
190			RowBox[{"r", " ",
191			RowBox[{"Switch", "[",
192			RowBox[{"\[Alpha]", ",", " ", "\[IndentingNewLine]", "1", ",",
193			RowBox[{
194			RowBox[{"Sin", "[", "\[Theta]", "]"}],
195			RowBox[{"Cos", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
196			"2", ",",
197			RowBox[{
198			RowBox[{"Sin", "[", "\[Theta]", "]"}],
199			RowBox[{"Sin", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
200			"3", ",",
201			RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}]}],
202			";"}], "\[IndentingNewLine]",
203			RowBox[{
204			RowBox[{
205			RowBox[{"T", "[",
206			RowBox[{"\[Alpha]_", ",", "\[Beta]_", ",", " ", "method_"}], "]"}], " ", ":=",
207			" ",
208			RowBox[{
209			RowBox[{
210			RowBox[{"KroneckerDelta", "[",
211			RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "*", " ",
212			RowBox[{"(",
213			RowBox[{
214			RowBox[{"v11", "[",
215			RowBox[{"r", ",", "method"}], "]"}], "/", "r"}], ")"}]}], "+", " ",
216			RowBox[{
217			RowBox[{"R", "[", "\[Alpha]", "]"}],
218			RowBox[{"R", "[", "\[Beta]", "]"}],
219			RowBox[{
220			RowBox[{"(",
221			RowBox[{
222			RowBox[{"v11prime", "[",
223			RowBox[{"r", ",", "method"}], "]"}], "-",
224			RowBox[{
225			RowBox[{"v11", "[",
226			RowBox[{"r", ",", "method"}], "]"}], "/", "r"}]}], ")"}], "/",
227			RowBox[{"r", "^", "2"}]}]}]}]}], ";"}], "\[IndentingNewLine]",
228			RowBox[{
229			RowBox[{"TBare", " ", "=", " ",
230			RowBox[{"MatrixForm", "[",
231			RowBox[{"Table", "[",
232			RowBox[{
233			RowBox[{"Table", "[",
234			RowBox[{
235			RowBox[{"Integrate", "[",
236			RowBox[{
237			RowBox[{
238			RowBox[{"r", "^", "2"}],
239			RowBox[{"Integrate", "[",
240			RowBox[{
241			RowBox[{"Integrate", "[",
242			RowBox[{
243			RowBox[{
244			RowBox[{"Sin", "[", "\[Theta]", "]"}],
245			RowBox[{"T", "[",
246			RowBox[{"i", ",", "j", ",", "BARE"}], "]"}]}], ",",
247			RowBox[{"{",
248			RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
249			",",
250			RowBox[{"{",
251			RowBox[{"\[Phi]", ",", "0", ",",
252			RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
253			RowBox[{"{",
254			RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
255			RowBox[{"{",
256			RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
257			RowBox[{"{",
258			RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
259			";"}], "\[IndentingNewLine]",
260			RowBox[{
261			RowBox[{"TSP", " ", "=", " ",
262			RowBox[{"MatrixForm", "[",
263			RowBox[{"Table", "[",
264			RowBox[{
265			RowBox[{"Table", "[",
266			RowBox[{
267			RowBox[{"Integrate", "[",
268			RowBox[{
269			RowBox[{
270			RowBox[{"r", "^", "2"}],
271			RowBox[{"Integrate", "[",
272			RowBox[{
273			RowBox[{"Integrate", "[",
274			RowBox[{
275			RowBox[{
276			RowBox[{"Sin", "[", "\[Theta]", "]"}],
277			RowBox[{"T", "[",
278			RowBox[{"i", ",", "j", ",", "SP"}], "]"}]}], ",",
279			RowBox[{"{",
280			RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
281			",",
282			RowBox[{"{",
283			RowBox[{"\[Phi]", ",", "0", ",",
284			RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
285			RowBox[{"{",
286			RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
287			RowBox[{"{",
288			RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
289			RowBox[{"{",
290			RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
291			";"}], "\[IndentingNewLine]",
292			RowBox[{
293			RowBox[{"TGSF", " ", "=", " ",
294			RowBox[{"MatrixForm", "[",
295			RowBox[{"Table", "[",
296			RowBox[{
297			RowBox[{"Table", "[",
298			RowBox[{
299			RowBox[{"Integrate", "[",
300			RowBox[{
301			RowBox[{
302			RowBox[{"r", "^", "2"}],
303			RowBox[{"Integrate", "[",
304			RowBox[{
305			RowBox[{"Integrate", "[",
306			RowBox[{
307			RowBox[{
308			RowBox[{"Sin", "[", "\[Theta]", "]"}],
309			RowBox[{"T", "[",
310			RowBox[{"i", ",", "j", ",", "GSF"}], "]"}]}], ",",
311			RowBox[{"{",
312			RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
313			",",
314			RowBox[{"{",
315			RowBox[{"\[Phi]", ",", "0", ",",
316			RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
317			RowBox[{"{",
318			RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
319			RowBox[{"{",
320			RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
321			RowBox[{"{",
322			RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
323			";"}], "\[IndentingNewLine]",
324			RowBox[{
325			RowBox[{"TTSF", " ", "=", " ",
326			RowBox[{"MatrixForm", "[",
327			RowBox[{"Table", "[",
328			RowBox[{
329			RowBox[{"Table", "[",
330			RowBox[{
331			RowBox[{"Integrate", "[",
332			RowBox[{
333			RowBox[{
334			RowBox[{"r", "^", "2"}],
335			RowBox[{"Integrate", "[",
336			RowBox[{
337			RowBox[{"Integrate", "[",
338			RowBox[{
339			RowBox[{
340			RowBox[{"Sin", "[", "\[Theta]", "]"}],
341			RowBox[{"T", "[",
342			RowBox[{"i", ",", "j", ",", "TSF"}], "]"}]}], ",",
343			RowBox[{"{",
344			RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
345			",",
346			RowBox[{"{",
347			RowBox[{"\[Phi]", ",", "0", ",",
348			RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
349			RowBox[{"{",
350			RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
351			RowBox[{"{",
352			RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
353			RowBox[{"{",
354			RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
355			";"}], "\[IndentingNewLine]",
356			RowBox[{
357			RowBox[{"QBARE", " ", "=",
358			RowBox[{"3",
359			RowBox[{
360			RowBox[{"Part", "[",
361			RowBox[{"TBare", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
362			RowBox[{"(",
363			RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
364			RowBox[{
365			RowBox[{"QTSP", " ", "=", " ",
366			RowBox[{"3",
367			RowBox[{
368			RowBox[{"Part", "[",
369			RowBox[{"TSP", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
370			RowBox[{"(",
371			RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
372			RowBox[{
373			RowBox[{"QGSF", " ", "=", " ",
374			RowBox[{"3",
375			RowBox[{
376			RowBox[{"Part", "[",
377			RowBox[{"TGSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
378			RowBox[{"(",
379			RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
380			RowBox[{
381			RowBox[{"QTSF", " ", "=", " ",
382			RowBox[{"3",
383			RowBox[{
384			RowBox[{"Part", "[",
385			RowBox[{"TTSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
386			RowBox[{"(",
387			RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}]}], "Input",
388			CellChangeTimes->{{3.613731558054296^9, 3.613732200209785^9},
389			3.6137322781282454`^9, {3.61373233169027^9, 3.613732397354877*^9}, {
390			3.613732488348338^9, 3.6137327713906393`^9}, {3.613732810835518*^9,
391			3.613732821957967^9}, {3.613732862763562^9, 3.613732913141625*^9}, {
392			3.61373295595298^9, 3.613733106904414^9}, {3.613733177027177*^9,
393			3.613733199740512^9}, {3.61373326352699^9, 3.6137332727080936`*^9}, {
394			3.613733425731758^9, 3.6137335719815893`^9}, {3.613733605778666*^9,
395			3.613733648768111^9}, {3.613733776819376^9, 3.6137338150569887`*^9}, {
396			3.6137338699918118`^9, 3.61373393057332^9}, {3.613733985426153*^9,
397			3.613733985628289^9}, {3.613734054134171^9, 3.6137340588514023`*^9}, {
398			3.6137371511302147`^9, 3.613737188118826^9}, {3.613815304031159*^9,
399			3.613815306899302^9}, {3.613815415274508^9, 3.613815450160325*^9}, {
400			3.613815535717202^9, 3.613815604127789^9}, {3.613815665097225*^9,
401			3.613815673383039^9}, {3.613816023942026^9, 3.6138160527230864`*^9}, {
402			3.613825536655637^9, 3.613825555245915^9}, {3.613825660601698*^9,
403			3.6138256692518787`^9}, {3.613825968874196^9, 3.613826000721004*^9}, {
404			3.6138263115515537`^9, 3.613826312408416^9}, {3.613826919678602*^9,
405			3.613826920319913^9}, {3.613827178556149^9, 3.6138272197490597`*^9}, {
406			3.6138410090125504`^9, 3.613841090576209^9}, {3.613841142597171*^9,
407			3.613841191624243^9}, {3.6138412274048777`^9, 3.613841229484283*^9}, {
408			3.6138413897003736`^9, 3.613841438224633^9}, {3.61384150925097*^9,
409			3.6138415133903227`^9}, {3.613841547354535^9, 3.613841573983226*^9}, {
410			3.613898318732862^9, 3.613898326606717^9}, {3.614440844373805*^9,
411			3.614440869838758^9}, {3.61444103194166^9, 3.614441084299322*^9}, {
412			3.614441116069621^9, 3.614441164401059^9}, {3.6144412214281187`*^9,
413			3.614441279916031^9}, {3.6144413160863132`^9, 3.614441341635235*^9}, {
414			3.614441394376206^9, 3.614441421059911^9}, {3.6144416231023483`*^9,
415			3.614441625159938^9}, {3.614442650450296^9, 3.6144427006914186`*^9}, {
416			3.614442735072257^9, 3.614442776902771^9}, {3.614442819684997*^9,
417			3.614442867826069^9}, {3.614442914658215^9, 3.614442924512073*^9}}],
418
419			Cell[CellGroupData[{
420
421			Cell[BoxData["QBARE"], "Input",
422			CellChangeTimes->{{3.61389845863691^9, 3.6138984602794447`^9}}],
423
424			Cell[BoxData[
425			FractionBox[
426			RowBox[{"3", " ",
427			RowBox[{"(",
428			RowBox[{
429			RowBox[{
430			RowBox[{"-",
431			FractionBox["8", "3"]}], " ",
432			SuperscriptBox["\[ExponentialE]",
433			RowBox[{
434			RowBox[{"-",
435			SuperscriptBox["rc", "2"]}], " ",
436			SuperscriptBox["\[Kappa]", "2"]}]], " ",
437			SqrtBox["\[Pi]"], " ", "rc", " ", "\[Kappa]"}], "+",
438			RowBox[{
439			FractionBox["4", "3"], " ", "\[Pi]", " ",
440			RowBox[{"Erf", "[",
441			RowBox[{"rc", " ", "\[Kappa]"}], "]"}]}]}], ")"}]}],
442			RowBox[{"4", " ", "\[Pi]"}]]], "Output",
443			CellChangeTimes->{
444			3.61389846058971^9, {3.6144418380848494`^9, 3.614441838682383*^9}, {
445			3.614443124832337^9, 3.614443142122366^9}}]
446			}, Open ]],
447
448			Cell[CellGroupData[{
449
450			Cell[BoxData["QTSP"], "Input",
451			CellChangeTimes->{{3.613898461774685^9, 3.61389846255107^9}}],
452
453			Cell[BoxData["1"], "Output",
454			CellChangeTimes->{3.6138984628297167`^9, 3.614441838710091^9,
455			3.614443128936681*^9}]
456			}, Open ]],
457
458			Cell[CellGroupData[{
459
460			Cell[BoxData[
461			RowBox[{"QGSF", " "}]], "Input",
462			CellChangeTimes->{{3.613898464699469^9, 3.613898465498917^9}, {
463			3.614441850430952^9, 3.6144418663262777`^9}, 3.61444313552145*^9}],
464
465			Cell[BoxData["1"], "Output",
466			CellChangeTimes->{
467			3.613898465771669^9, {3.614441838760746^9, 3.614441866820423*^9}, {
468			3.614443131316518^9, 3.614443135852601^9}}]
469			}, Open ]],
470
471			Cell[CellGroupData[{
472
473			Cell[BoxData["QTSF"], "Input",
474			CellChangeTimes->{{3.613898466555105^9, 3.613898468075191^9}}],
475
476			Cell[BoxData["1"], "Output",
477			CellChangeTimes->{3.613898468428026^9, 3.614441838800758^9,
478			3.614443138734713*^9}]
479			}, Open ]],
480
481			Cell[CellGroupData[{
482
483			Cell[BoxData[
484			RowBox[{"FullSimplify", "[", "QTSP", "]"}]], "Input",
485			CellChangeTimes->{{3.613898477301433^9, 3.613898481802129^9}}],
486
487			Cell[BoxData["1"], "Output",
488			CellChangeTimes->{3.613898482310692^9, 3.614441838849948^9}]
489			}, Open ]]
490			},
491			WindowSize->{884, 1337},
492			WindowMargins->{{500, Automatic}, {Automatic, 0}},
493			FrontEndVersion->"10.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 27, \
494			2014)",
495			StyleDefinitions->"Default.nb"
496			]
497			(* End of Notebook Content *)
498
499			(* Internal cache information *)
500			(*CellTagsOutline
501			CellTagsIndex->{}
502			*)
503			(*CellTagsIndex
504			CellTagsIndex->{}
505			*)
506			(*NotebookFileOutline
507			Notebook[{
508			Cell[557, 20, 14650, 396, 811, "Input"],
509			Cell[CellGroupData[{
510			Cell[15232, 420, 98, 1, 28, "Input"],
511			Cell[15333, 423, 719, 21, 58, "Output"]
512			}, Open ]],
513			Cell[CellGroupData[{
514			Cell[16089, 449, 95, 1, 28, "Input"],
515			Cell[16187, 452, 119, 2, 28, "Output"]
516			}, Open ]],
517			Cell[CellGroupData[{
518			Cell[16343, 459, 186, 3, 28, "Input"],
519			Cell[16532, 464, 169, 3, 28, "Output"]
520			}, Open ]],
521			Cell[CellGroupData[{
522			Cell[16738, 472, 96, 1, 28, "Input"],
523			Cell[16837, 475, 117, 2, 28, "Output"]
524			}, Open ]],
525			Cell[CellGroupData[{
526			Cell[16991, 482, 134, 2, 28, "Input"],
527			Cell[17128, 486, 92, 1, 28, "Output"]
528			}, Open ]]
529			}
530			]
531			*)
532
533			(* End of internal cache information *)