File:2D Spherical Harmonic Orbitals.png

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(1,524 × 3,778 pixels, file size: 1.19 MB, MIME type: image/png)

Captions

Captions

Add a one-line explanation of what this file represents

Summary[edit]

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[edit]

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[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
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

Click on a date/time to view the file as it appeared at that time.

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

You cannot overwrite this file.

There are no pages that use this file.

File usage on other wikis

The following other wikis use this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:2D_Spherical_Harmonic_Orbitals.png&oldid=766987620"