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Summary

Description
English: Schrödinger 3D Spherical Harmonic Orbital solutions in 2D Density plots with Mathematica(TM) generating source code snippet at the top. This is constructed from VisibLie_E8 found on TheoryOfEverything.org
Date
Source See below for mathematica source code Own work
Author Jgmoxness
PNG development
InfoField
 
This diagram was created with Mathematica.

Source code

The following code was rewritten manually based on the one embedded in the picture. It differes only in small conventions (for instance it doesn't use the subscription notation). Furthermore, a bug has been replaced (phi = arc tan(x,y) instead phi = arc tan (x,0)^2)

ClearAll[detail, R, Y, \[Psi], orb];
detail[n_, l_, m_] := 8 Total@{n, l, m}
F[n_, l_, x_ ] := 
  x^l Exp[-x/2] Factorial[n + 1] LaguerreL[n - l - 1, 2 l + 1, x];
R[n_ , l_, r_, 
   a_] := (2/(n a))^2 Sqrt[ a/4 (n - l - 1)!/((n + 1)!)^3] F[n, l, (
    2 r)/(n a)];
Y = SphericalHarmonicY;
\[Psi][n_ , l_, m_, r_, a_, \[Theta]_, \[Phi]_] := 
 R[n, l, r, a] Abs@Y[l, m, \[Theta], \[Phi]]
orb[n_, l_, m_, x_, y_, z_] := Module[{r = Norm@{x, y, z}},
   \[Psi][n, l, m, r, 1(*a*), ArcCos[z/r], ArcTan[x, y]]];
orbDensity[n_, l_, m_] := DensityPlot[orb[n, l, m, x, 0 (* doing a 2d cut in y=0 *), z],
  {x, -detail[n, l, m], detail[n, l, m]}, {z, -detail[n, l, m], 
   detail[n, l, m]}, 
  Mesh -> False, Frame -> False, PlotPoints -> 45, 
  ColorFunctionScaling -> True, ColorFunction -> "SunsetColors"]
MatrixForm@
 Table[MatrixForm@
   Table[Row@Table[{{n, l, m}, orbDensity[n, l, m]}, {m, 0, l}], {l, 
     0, n - 1}], {n, 1, 3}]

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26 May 2013

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Date/TimeThumbnailDimensionsUserComment
current14:37, 28 June 2017Thumbnail for version as of 14:37, 28 June 20171,524 × 3,778 (1.19 MB)Jgmoxnessbetter resolution
14:29, 28 June 2017Thumbnail for version as of 14:29, 28 June 2017413 × 1,024 (327 KB)JgmoxnessUser created page with UploadWizard

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