Image:SH Real (3,3).gif

Description	The real part of the spherical harmonic with l=3, m=3.
Source	Self Made This mathematical image was created with Mathematica.
Date	03/06/2007
Author	Inductiveload
Permission (Reusing this image)	see below
Other versions	Version with legend

Mathematical Function Plot
Description	Real Spherical harmonic, m=3, l=3.
Equation
Co-ordinate System	Spherical
Plot Type	Density
Notes	Yellow is large and positive Blue is large and negative

[edit] Mathematica Code

This code requires a special module called "SphericalDensityPlot3Dmod2.m" to run. It is a small modification of code by Florian Berger. The module code can be found here, along with instructions on how to install the module.

<< SphericalDensityPlot3Dmod2.m
Clear[l, m, sph, sh];
l = 3; (*Parameters of SH*)
m = 3;

Table[
  phi = ph + k Pi/24; (*Increments of phi - 48/revolution*)
  If[m > 0,
    sph := (1/Sqrt[2])(SphericalHarmonicY[l, 
    m, th, phi] + (-1)^m SphericalHarmonicY[l, -m, th, phi]), (*Case m > 0*)
    If[m < 0, (*then m <= 0*)
      sph := (1/I Sqrt[2])(
    SphericalHarmonicY[
      l, -m, th, phi] - (-1)^-m SphericalHarmonicY[l, m, th, phi]), (*Case 
              m > 0*)
      sph := SphericalHarmonicY[l, m, th, phi]]]; (*Case m = 0*)(*End If, End 
                If*)
  sh = SphericalDensityPlot3D[
      Re[sph],
      {th, 0, Pi}, (*Theta range*)
      {ph, 0, 2Pi}, (*Phi range*)
      PlotPoints -> {20, 40}, (*Resolution*)
      LegendOff -> True,
      Axes -> False,
      Boxed -> False,
      ViewPoint -> {-0, -10, -0},
      ImageSize -> 300];
  num = StringJoin[Map[ToString[#] &, IntegerDigits[k, 10, 2]]]; (*Gives a 
      number string of width 2 for easier ordering*)
  str = "SH(" <> ToString[l] <> "," <> ToString[m] <> ") " <> num <> 
      ".gif"; (*Constructs a name for the frame*)
  Export[str, sh],   (*Export the frame*)
  {k, 0, 15, 1}]

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