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

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

(* CreatedBy='Mathematica 11.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     15808,        455]
NotebookOptionsPosition[     14428,        417]
NotebookOutlinePosition[     14772,        432]
CellTagsIndexPosition[     14729,        429]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Fun\[CCedilla]\[OTilde]es de onda do \[AAcute]tomo de H", "Title",
 CellChangeTimes->{{3.721165934677552*^9, 3.721165942240858*^9}}],

Cell["Prof. jose antonio diaz navas, no Mathematica Stack Exchange", "Text",
 CellChangeTimes->{{3.7211659656438894`*^9, 
  3.7211659824819994`*^9}},ExpressionUUID->"a0c929a5-a8a1-4bf0-aea1-\
510978e79416"],

Cell[BoxData[
 RowBox[{"a0", "=", 
  RowBox[{
   RowBox[{"Quantity", "[", "\"\<BohrRadius\>\"", "]"}], "/", 
   RowBox[{"Quantity", "[", "\"\<Meters\>\"", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7211656023206496`*^9, 3.7211656244863653`*^9}, 
   3.7214019684377646`*^9},ExpressionUUID->"346e01ae-2c5e-482c-a649-\
c59835cd1ce4"],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Psi]", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"n_", ",", "l_", ",", "m_"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"r_", ",", "\[Theta]_", ",", "\[Phi]_"}], "}"}]}], "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"\[Rho]", "=", 
      RowBox[{"2", " ", 
       RowBox[{"r", "/", 
        RowBox[{"(", 
         RowBox[{"n", " ", "a0"}], ")"}]}]}]}], "}"}], ",", 
    RowBox[{
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{"2", "/", 
          RowBox[{"(", 
           RowBox[{"n", " ", "a0"}], ")"}]}], ")"}], "^", "3"}], " ", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"n", "-", "l", "-", "1"}], ")"}], "!"}], "/", 
        RowBox[{"(", 
         RowBox[{"2", " ", "n", " ", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{"n", "+", "l"}], ")"}], "!"}]}], ")"}]}]}], "]"}], " ", 
     RowBox[{"Exp", "[", 
      RowBox[{
       RowBox[{"-", "\[Rho]"}], "/", "2"}], "]"}], " ", 
     RowBox[{"\[Rho]", "^", "l"}], " ", 
     RowBox[{"LaguerreL", "[", 
      RowBox[{
       RowBox[{"n", "-", "l", "-", "1"}], ",", 
       RowBox[{
        RowBox[{"2", " ", "l"}], "+", "1"}], ",", "\[Rho]"}], "]"}], " ", 
     RowBox[{"SphericalHarmonicY", "[", 
      RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[Phi]"}], "]"}]}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.7211656113569326`*^9, 3.721165618683462*^9}, {
   3.7214020293347116`*^9, 3.721402033475766*^9}, 3.721402072917361*^9, {
   3.72140240027355*^9, 3.7214024045552444`*^9}, {3.721402745727668*^9, 
   3.7214027495405636`*^9}},ExpressionUUID->"e44b86ff-0c87-4ac4-b39e-\
9f4b4ebfcaca"],

Cell[BoxData[
 RowBox[{
  RowBox[{"n", "=", "2"}], ";", 
  RowBox[{"l", "=", "0"}], ";", 
  RowBox[{"m", "=", "0"}]}]], "Input",
 CellChangeTimes->{{3.7211657222420893`*^9, 3.721165730097622*^9}, {
   3.7211659962322397`*^9, 3.721165996716389*^9}, {3.7211660480713043`*^9, 
   3.7211661475592976`*^9}, {3.721402097329753*^9, 3.721402135572961*^9}, {
   3.721402427838912*^9, 3.721402437418031*^9}, 3.7214027647765203`*^9, {
   3.721402827269621*^9, 
   3.7214028414885483`*^9}},ExpressionUUID->"9822649a-1a50-4171-bfac-\
f5bcc4744bd6"],

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "=", 
   RowBox[{"TransformedField", "[", 
    RowBox[{
     RowBox[{"\"\<Spherical\>\"", "\[Rule]", "\"\<Cartesian\>\""}], ",", 
     RowBox[{"\[Psi]", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", "l", ",", "m"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], "]"}], ",", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}], "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.7211656153449807`*^9, 
  3.7211656328501368`*^9}},ExpressionUUID->"931e32a4-64f8-4bf2-a8b3-\
9148115eab05"],

Cell[BoxData[
 RowBox[{"DensityPlot3D", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"Abs", "@", "f"}], ")"}], "^", "2"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{
      RowBox[{"-", "20"}], " ", "a0"}], ",", 
     RowBox[{"20", " ", "a0"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{
      RowBox[{"-", "20"}], " ", "a0"}], ",", 
     RowBox[{"20", " ", "a0"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"z", ",", 
     RowBox[{
      RowBox[{"-", "20"}], " ", "a0"}], ",", 
     RowBox[{"20", " ", "a0"}]}], "}"}], ",", 
   RowBox[{"RegionFunction", "\[Rule]", 
    RowBox[{"Function", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", 
      RowBox[{
       RowBox[{"x", "<", "0"}], "||", 
       RowBox[{"y", ">", "0"}]}]}], "]"}]}], ",", 
   RowBox[{"ColorFunction", "\[Rule]", "Hue"}], ",", 
   RowBox[{"ColorFunctionScaling", "\[Rule]", "True"}], ",", 
   RowBox[{"ViewPoint", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"1.3", ",", 
      RowBox[{"-", "2.4"}], ",", "1."}], "}"}]}], ",", 
   RowBox[{"FaceGrids", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", 
        RowBox[{"-", "1"}]}], "}"}]}], "}"}]}], ",", 
   RowBox[{"Ticks", "\[Rule]", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "20"}], " ", "a0"}], ",", "\"\<-20 a0\>\""}], "}"}], 
        ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "10"}], " ", "a0"}], ",", "\"\<-10 a0\>\""}], "}"}], 
        ",", 
        RowBox[{"{", 
         RowBox[{"0", ",", "\"\<0\>\""}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"10", " ", "a0"}], ",", "\"\<10 a0\>\""}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"20", " ", "a0"}], ",", "\"\<20 a0\>\""}], "}"}]}], "}"}], 
      ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "3"}], "}"}]}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7211656544744835`*^9, 3.7211656544744835`*^9}, {
  3.7214028896900907`*^9, 
  3.721402893848381*^9}},ExpressionUUID->"a0eff236-22ad-439d-bfe4-\
37f2c311981c"],

Cell[BoxData[
 RowBox[{"Integrate", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"\[Psi]", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"n", ",", "l", ",", "m"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], "]"}], "*", 
    RowBox[{"Conjugate", "[", 
     RowBox[{"\[Psi]", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", "l", ",", "m"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], "]"}], "]"}], 
    RowBox[{"r", "^", "2"}], " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[Phi]", ",", "0", ",", 
     RowBox[{"2", "Pi"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.721402165108513*^9, 
  3.721402289918344*^9}},ExpressionUUID->"a56b0f96-f7eb-41fa-b02d-\
4c5afcf4f39e"],

Cell[BoxData[
 RowBox[{"Integrate", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Abs", "[", 
      RowBox[{"\[Psi]", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"n", ",", "l", ",", "m"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], "]"}], " ", 
      "]"}], "^", "2"}], "  ", 
    RowBox[{"r", "^", "2"}], " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[Phi]", ",", "0", ",", 
     RowBox[{"2", "Pi"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7214025741978564`*^9, 3.7214025920903378`*^9}, 
   3.7214027764112577`*^9},ExpressionUUID->"04ef3379-b332-4875-811b-\
f0aff73634f1"],

Cell[CellGroupData[{

Cell["Manipulate interface", "Subsection",
 CellChangeTimes->{{3.721402869677408*^9, 
  3.7214028822568398`*^9}},ExpressionUUID->"de7e8ace-f958-4468-80b0-\
ed49836c3b74"],

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "f", ",", "feLabel", ",", "feLabel2", ",", "feLabelm", ",", 
       "feLabel2m"}], "}"}], ",", 
     RowBox[{
      RowBox[{"f", "=", 
       RowBox[{"TransformedField", "[", 
        RowBox[{
         RowBox[{"\"\<Spherical\>\"", "\[Rule]", "\"\<Cartesian\>\""}], ",", 
         RowBox[{
          RowBox[{"Abs", "[", 
           RowBox[{"\[Psi]", "[", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{"n", ",", "l", ",", "m"}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], "]"}], 
           "]"}], "^", "2"}], ",", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}], "\[Rule]", 
          RowBox[{"{", 
           RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"feLabel", "=", 
       RowBox[{"StringJoin", "[", 
        RowBox[{
         RowBox[{"ToString", "[", "fe", "]"}], ",", "\"\< a0\>\""}], "]"}]}], 
      ";", "\[IndentingNewLine]", 
      RowBox[{"feLabel2", "=", 
       RowBox[{"StringJoin", "[", 
        RowBox[{
         RowBox[{"ToString", "[", 
          RowBox[{"fe", "/", "2"}], "]"}], ",", "\"\< a0\>\""}], "]"}]}], ";",
       "\[IndentingNewLine]", 
      RowBox[{"feLabelm", "=", 
       RowBox[{"StringJoin", "[", 
        RowBox[{"\"\<-\>\"", ",", 
         RowBox[{"ToString", "[", "fe", "]"}], ",", "\"\< a0\>\""}], "]"}]}], 
      ";", "\[IndentingNewLine]", 
      RowBox[{"feLabel2m", "=", 
       RowBox[{"StringJoin", "[", 
        RowBox[{"\"\<-\>\"", ",", 
         RowBox[{"ToString", "[", 
          RowBox[{"fe", "/", "2"}], "]"}], ",", "\"\< a0\>\""}], "]"}]}], ";",
       "\[IndentingNewLine]", 
      RowBox[{"DensityPlot3D", "[", 
       RowBox[{"f", ",", 
        RowBox[{"{", 
         RowBox[{"x", ",", 
          RowBox[{
           RowBox[{"-", "fe"}], " ", "a0"}], ",", 
          RowBox[{"fe", " ", "a0"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"y", ",", 
          RowBox[{
           RowBox[{"-", "fe"}], " ", "a0"}], ",", 
          RowBox[{"fe", " ", "a0"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"z", ",", 
          RowBox[{
           RowBox[{"-", "fe"}], " ", "a0"}], ",", 
          RowBox[{"fe", " ", "a0"}]}], "}"}], ",", 
        RowBox[{"RegionFunction", "\[Rule]", 
         RowBox[{"Function", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", 
           RowBox[{
            RowBox[{"x", "<", "0"}], "||", 
            RowBox[{"y", ">", "0"}]}]}], "]"}]}], ",", 
        RowBox[{"ColorFunction", "\[Rule]", "Hue"}], ",", 
        RowBox[{"ColorFunctionScaling", "\[Rule]", "True"}], ",", 
        RowBox[{"ViewPoint", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{"1.3", ",", 
           RowBox[{"-", "2.4"}], ",", "1."}], "}"}]}], ",", 
        RowBox[{"FaceGrids", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", 
             RowBox[{"-", "1"}]}], "}"}]}], "}"}]}], ",", 
        RowBox[{"Ticks", "\[Rule]", 
         RowBox[{"Table", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "fe"}], " ", "a0"}], ",", "feLabelm"}], "}"}], 
             ",", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "fe"}], " ", 
                RowBox[{"a0", "/", "2"}]}], ",", "feLabel2m"}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"0", ",", "\"\<0\>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"fe", " ", 
                RowBox[{"a0", "/", "2"}]}], ",", "feLabel2"}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"fe", " ", "a0"}], ",", "feLabel"}], "}"}]}], "}"}], 
           ",", 
           RowBox[{"{", 
            RowBox[{"i", ",", "3"}], "}"}]}], "]"}]}]}], "]"}]}]}], "]"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", "1"}], "}"}], ",", "1", ",", "5", ",", "1"}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"l", ",", "0"}], "}"}], ",", "0", ",", 
     RowBox[{"n", "-", "1"}], ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"m", ",", "0"}], "}"}], ",", "0", ",", "l", ",", "1"}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"fe", ",", "20"}], "}"}], ",", "2", ",", "40", ",", "2"}], 
    "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.721402898692634*^9, 3.7214029890767384`*^9}, {
  3.7214030243438244`*^9, 3.721403044842698*^9}, {3.721403090247077*^9, 
  3.721403112788761*^9}, {3.7214032090467997`*^9, 3.7214032211992254`*^9}, {
  3.721403447704734*^9, 3.7214034625500245`*^9}, {3.7214036274455476`*^9, 
  3.7214036399735503`*^9}, {3.7214036764203205`*^9, 3.7214037685669355`*^9}, {
  3.7214039628398523`*^9, 3.7214040055740232`*^9}, {3.721404085738321*^9, 
  3.7214041678057504`*^9}, {3.7214042205328064`*^9, 
  3.721404315178094*^9}},ExpressionUUID->"1e40c05a-482e-4de6-a3c4-\
acf5b914f0a4"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{759, 765},
WindowMargins->{{482, Automatic}, {97, Automatic}},
FrontEndVersion->"11.1 for Microsoft Windows (64-bit) (April 18, 2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 138, 1, 101, "Title", "ExpressionUUID" -> \
"b169dac2-6dfa-4234-ba27-dfd2d53a31c4"],
Cell[721, 25, 206, 3, 30, "Text", "ExpressionUUID" -> \
"a0c929a5-a8a1-4bf0-aea1-510978e79416"],
Cell[930, 30, 330, 7, 30, "Input", "ExpressionUUID" -> \
"346e01ae-2c5e-482c-a649-c59835cd1ce4"],
Cell[1263, 39, 1731, 49, 69, "Input", "ExpressionUUID" -> \
"e44b86ff-0c87-4ac4-b39e-9f4b4ebfcaca"],
Cell[2997, 90, 535, 11, 30, "Input", "ExpressionUUID" -> \
"9822649a-1a50-4171-bfac-f5bcc4744bd6"],
Cell[3535, 103, 723, 19, 30, "Input", "ExpressionUUID" -> \
"931e32a4-64f8-4bf2-a8b3-9148115eab05"],
Cell[4261, 124, 2455, 75, 126, "Input", "ExpressionUUID" -> \
"a0eff236-22ad-439d-bfe4-37f2c311981c"],
Cell[6719, 201, 1003, 28, 50, "Input", "ExpressionUUID" -> \
"a56b0f96-f7eb-41fa-b02d-4c5afcf4f39e"],
Cell[7725, 231, 863, 24, 50, "Input", "ExpressionUUID" -> \
"04ef3379-b332-4875-811b-f0aff73634f1"],
Cell[CellGroupData[{
Cell[8613, 259, 170, 3, 49, "Subsection", "ExpressionUUID" -> \
"de7e8ace-f958-4468-80b0-ed49836c3b74"],
Cell[8786, 264, 5614, 149, 278, "Input", "ExpressionUUID" -> \
"1e40c05a-482e-4de6-a3c4-acf5b914f0a4"]
}, Open  ]]
}, Open  ]]
}
]
*)