File:2D Spherical Harmonic Orbitals.png
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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 |  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}]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- to share – to copy, distribute and transmit the work
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- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:37, 28 June 2017 | | 1,524 × 3,778 (1.19 MB) | Jgmoxness | better resolution |
| 14:29, 28 June 2017 |  | 413 × 1,024 (327 KB) | Jgmoxness | User created page with UploadWizard |
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