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WindowTitle->Plots of Quantum Probability Density Functions in the Hydrogen \
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         "]; $CellContext`cosinus[0, 0] = Table[
          
          Random[], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[1, 0] = 
        Table[Random[]^(1/3), {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`prov = Table[
          
          Random[], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[1, 1] = 
        Chop[(1 - I 
           Sqrt[3] + (1 + 
             I Sqrt[3]) ($CellContext`prov + Sqrt[-1 + $CellContext`prov^2])^(
              2/3))/(2 ($CellContext`prov + Sqrt[-1 + $CellContext`prov^2])^(
            1/3))]; $CellContext`cosinus[2, 0] = Table[
          Part[
           
           FindRoot[(-4) Random[] + 5 $CellContext`u - 10 $CellContext`u^3 + 
             9 $CellContext`u^5 == 0, {$CellContext`u, 0, 1}], 1, 
           2], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[2, 1] = Table[
          Part[
           FindRoot[
           2 Random[] - 5 $CellContext`u^3 + 3 $CellContext`u^5 == 
            0, {$CellContext`u, 0, 1}], 1, 2], {$CellContext`i, 
           1, $CellContext`Nmax/4}]; $CellContext`cosinus[2, 2] = Table[
          Part[
           
           FindRoot[(-8) Random[] + 15 $CellContext`u - 10 $CellContext`u^3 + 
             3 $CellContext`u^5 == 0, {$CellContext`u, 0, 1}], 1, 
           2], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[3, 0] = Table[
          Part[
           
           FindRoot[(-4) Random[] + 21 $CellContext`u^3 - 42 $CellContext`u^5 + 
             25 $CellContext`u^7 == 0, {$CellContext`u, 0, 1}], 1, 
           2], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[3, 1] = Table[
          Part[
           FindRoot[
           16 Random[] - 21 $CellContext`u + 77 $CellContext`u^3 - 
             147 $CellContext`u^5 + 75 $CellContext`u^7 == 
            0, {$CellContext`u, 0, 1}], 1, 2], {$CellContext`i, 
           1, $CellContext`Nmax/4}]; $CellContext`cosinus[3, 2] = Table[
          Part[
           
           FindRoot[(-8) Random[] + 35 $CellContext`u^3 - 42 $CellContext`u^5 + 
             15 $CellContext`u^7 == 0, {$CellContext`u, 0, 1}], 1, 
           2], {$CellContext`i, 1, $CellContext`Nmax/
           4}]; $CellContext`cosinus[3, 3] = Table[
          Part[
           FindRoot[
           16 Random[] - 35 $CellContext`u + 35 $CellContext`u^3 - 
             21 $CellContext`u^5 + 5 $CellContext`u^7 == 
            0, {$CellContext`u, 0, 1}], 1, 2], {$CellContext`i, 
           1, $CellContext`Nmax/4}]; $CellContext`Delta1 = 
        0.125; $CellContext`sign = 
        Table[2 RandomInteger[] - 
          1, {$CellContext`i, 1, $CellContext`Nmax}]; $CellContext`phinus = 
        Table[(2 Pi) 
          Random[], {$CellContext`i, 
           1, $CellContext`Nmax}]; $CellContext`sort1 = Table[
          
          RandomInteger[{1, $CellContext`Nmax/4}], {$CellContext`i, 
           1, $CellContext`Nmax}]; $CellContext`sort2 = Table[
          
          RandomInteger[{1, $CellContext`Nmax/4}], {$CellContext`i, 
           1, $CellContext`Nmax}]; 
       For[$CellContext`nn = 1, $CellContext`nn < 5, 
         Increment[$CellContext`nn], 
         For[$CellContext`ll = 0, $CellContext`ll < $CellContext`nn, 
          Increment[$CellContext`ll], 
          For[$CellContext`mm = 0, $CellContext`mm < $CellContext`ll + 1, 
           
           Increment[$CellContext`mm], $CellContext`table3D[$CellContext`nn, \
$CellContext`ll, $CellContext`mm] = Table[{(Part[
                  $CellContext`radius[$CellContext`nn, $CellContext`ll], 
                  Part[$CellContext`sort1, $CellContext`i]] Sqrt[1 - Part[
                    $CellContext`cosinus[$CellContext`ll, $CellContext`mm], 
                    Part[$CellContext`sort2, $CellContext`i]]^2]) Cos[
                 Part[$CellContext`phinus, $CellContext`i]], (Part[
                  $CellContext`radius[$CellContext`nn, $CellContext`ll], 
                  Part[$CellContext`sort1, $CellContext`i]] Sqrt[1 - Part[
                    $CellContext`cosinus[$CellContext`ll, $CellContext`mm], 
                    Part[$CellContext`sort2, $CellContext`i]]^2]) Sin[
                 Part[$CellContext`phinus, $CellContext`i]], (Part[
                  $CellContext`radius[$CellContext`nn, $CellContext`ll], 
                  Part[$CellContext`sort1, $CellContext`i]] Part[
                  $CellContext`cosinus[$CellContext`ll, $CellContext`mm], 
                  Part[$CellContext`sort2, $CellContext`i]]) 
               Part[$CellContext`sign, $CellContext`i]}, {$CellContext`i, \
$CellContext`Nmax}]; For[$CellContext`kk = 1, $CellContext`kk < 5, 
             
             Increment[$CellContext`kk], $CellContext`phi0 = $CellContext`kk (
                Pi/4); $CellContext`Delta = $CellContext`nn^2 \
$CellContext`Delta1; $CellContext`i = 1; 
             For[$CellContext`k = 1, $CellContext`k < $CellContext`Nmax + 1, 
               Increment[$CellContext`k], 
               If[(Part[
                    $CellContext`table3D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm], $CellContext`k, 1]^2 + Part[
                    $CellContext`table3D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm], $CellContext`k, 2]^2) 
                 Sin[$CellContext`phi0 - 
                    Part[$CellContext`phinus, $CellContext`k]]^2 < \
$CellContext`Delta^2, $CellContext`xx[$CellContext`i] = Sqrt[Part[
                    $CellContext`table3D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm], $CellContext`k, 1]^2 + Part[
                    $CellContext`table3D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm], $CellContext`k, 2]^2] 
                  Cos[$CellContext`phi0 - 
                    Part[$CellContext`phinus, $CellContext`k]]; \
$CellContext`zz[$CellContext`i] = Part[
                   $CellContext`table3D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm], $CellContext`k, 3]; $CellContext`i = $CellContext`i + 
                  1, $CellContext`i = $CellContext`i]]; \
$CellContext`imax[$CellContext`nn, $CellContext`ll, $CellContext`mm, \
$CellContext`kk] = $CellContext`i - 
               1; $CellContext`slice2D[$CellContext`nn, $CellContext`ll, \
$CellContext`mm, $CellContext`kk] = Table[{
                 $CellContext`xx[$CellContext`j], 
                 $CellContext`zz[$CellContext`j]}, {$CellContext`j, 1, 
                 $CellContext`imax[$CellContext`nn, $CellContext`ll, \
$CellContext`mm, $CellContext`kk]}]]]]]; $CellContext`xmax[1] = 
        5; $CellContext`xmax[2] = 15; $CellContext`xmax[3] = 
        30; $CellContext`xmax[4] = 45; $CellContext`pointsize = 
        0.005; $CellContext`Planes[
          Pattern[$CellContext`n$, 
           Blank[]], 
          Pattern[$CellContext`kk$, 
           Blank[]]] := If[$CellContext`kk$ < 5, 
          Graphics3D[
           Rotate[{Green, 
             Opacity[0.05], 
             
             Cuboid[{0, -$CellContext`xmax[$CellContext`n$], \
-$CellContext`xmax[$CellContext`n$]}, {0, 
               $CellContext`xmax[$CellContext`n$], 
               $CellContext`xmax[$CellContext`n$]}]}, $CellContext`kk$ (Pi/
             4), {0, 0, 1}, {0, 0, 0}], ImageSize -> {550, 350}], 
          Graphics3D[
           Table[
            Rotate[{Green, 
              Opacity[0.05], 
              
              Cuboid[{0, -$CellContext`xmax[$CellContext`n$], \
-$CellContext`xmax[$CellContext`n$]}, {0, 
                $CellContext`xmax[$CellContext`n$], 
                $CellContext`xmax[$CellContext`n$]}]}, $CellContext`jj$$ (Pi/
              4), {0, 0, 1}, {0, 0, 0}], {$CellContext`jj$$, 1, 4}], 
           ImageSize -> {550, 350}]]; $CellContext`View3D[
          Pattern[$CellContext`n, 
           Blank[]], 
          Pattern[$CellContext`l, 
           Blank[]], 
          Pattern[$CellContext`m, 
           Blank[]], 
          Pattern[$CellContext`kk, 
           Blank[]], 
          Pattern[$CellContext`NN, 
           Blank[]]] := If[$CellContext`kk == 0, 
          ListPointPlot3D[
           Table[
            Part[
             $CellContext`table3D[$CellContext`n, $CellContext`l, \
$CellContext`m], $CellContext`i], {$CellContext`i, 1, $CellContext`NN}], 
           BoxRatios -> {1, 1, 1}, AxesLabel -> {
             Style["x", Italic], 
             Style["y", Italic], 
             Style["z", Italic]}, PlotStyle -> 
           PointSize[$CellContext`pointsize], 
           PlotRange -> {{-$CellContext`xmax[$CellContext`n], 
              $CellContext`xmax[$CellContext`n]}, \
{-$CellContext`xmax[$CellContext`n], 
              $CellContext`xmax[$CellContext`n]}, \
{-$CellContext`xmax[$CellContext`n], 
              $CellContext`xmax[$CellContext`n]}}, 
           ViewPoint -> {1., -2.4, 1.}, ImageSize -> {550, 350}], 
          Show[
           ListPointPlot3D[
            Table[
             Part[
              $CellContext`table3D[$CellContext`n, $CellContext`l, \
$CellContext`m], $CellContext`i], {$CellContext`i, 1, $CellContext`NN}], 
            BoxRatios -> {1, 1, 1}, AxesLabel -> {
              Style["x", Italic], 
              Style["y", Italic], 
              Style["z", Italic]}, PlotStyle -> 
            PointSize[$CellContext`pointsize], 
            PlotRange -> {{-$CellContext`xmax[$CellContext`n], 
               $CellContext`xmax[$CellContext`n]}, \
{-$CellContext`xmax[$CellContext`n], 
               $CellContext`xmax[$CellContext`n]}, \
{-$CellContext`xmax[$CellContext`n], 
               $CellContext`xmax[$CellContext`n]}}, 
            ViewPoint -> {1., -2.4, 1.}, ImageSize -> {550, 350}], 
           $CellContext`Planes[$CellContext`n, $CellContext`kk]]]; \
$CellContext`hue = {0.1, 0.3, 0.7, 0.9}; $CellContext`ViewSlice[
          Pattern[$CellContext`n$, 
           Blank[]], 
          Pattern[$CellContext`l$, 
           Blank[]], 
          Pattern[$CellContext`m$, 
           Blank[]], 
          Pattern[$CellContext`kk$, 
           Blank[]], 
          Pattern[$CellContext`NN$, 
           Blank[]]] := If[$CellContext`kk$ == 0, 
          Style["Choose an orientation!", 30], 
          If[$CellContext`kk$ < 5, 
           ListPlot[
            Table[
             Part[
              $CellContext`slice2D[$CellContext`n$, $CellContext`l$, \
$CellContext`m$, $CellContext`kk$], $CellContext`i], {$CellContext`i, 
              1, $CellContext`imax[$CellContext`n$, $CellContext`l$, \
$CellContext`m$, $CellContext`kk$] ($CellContext`NN$/$CellContext`Nmax)}], 
            AspectRatio -> 1, PlotStyle -> {
              PointSize[$CellContext`pointsize], 
              Hue[
               Part[$CellContext`hue, $CellContext`kk$]]}, 
            PlotRange -> {{-$CellContext`xmax[$CellContext`n$], 
               $CellContext`xmax[$CellContext`n$]}, \
{-$CellContext`xmax[$CellContext`n$], 
               $CellContext`xmax[$CellContext`n$]}}, AxesLabel -> {
              Derivative[1][
               Style["x", Italic]], 
              Style["z", Italic]}, ImageSize -> {550, 350}], 
           Show[
            Table[
             $CellContext`ViewSlice[$CellContext`n$, $CellContext`l$, \
$CellContext`m$, $CellContext`jj$$, $CellContext`NN$], {$CellContext`jj$$, 1, 
              4}]]]]; $CellContext`View[
          Pattern[$CellContext`n, 
           Blank[]], 
          Pattern[$CellContext`l, 
           Blank[]], 
          Pattern[$CellContext`m, 
           Blank[]], 
          Pattern[$CellContext`kk, 
           Blank[]], 
          Pattern[$CellContext`NN, 
           Blank[]], 
          Pattern[$CellContext`f, 
           Blank[]]] := If[$CellContext`f == 1, 
          $CellContext`View3D[$CellContext`n, $CellContext`l, $CellContext`m, \
$CellContext`kk, $CellContext`NN], 
          $CellContext`ViewSlice[$CellContext`n, $CellContext`l, \
$CellContext`m, $CellContext`kk, $CellContext`NN]]; $CellContext`Viewoverm[
          Pattern[$CellContext`n, 
           Blank[]], 
          Pattern[$CellContext`l, 
           Blank[]], 
          Pattern[$CellContext`kk, 
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