SphericalPlot3D generates flat surfaces

Question

I'm trying to plot a function r(theta, phi) but having some difficulty. It's also possible that I've misinterpreted the paper I'm pulling these formula from, but I think I'm most likely making some error in Mathematica.

This is the function I'm trying to plot, and the plot that the authors were able to generate:

I'm using the code SphericalPlot3D[-2*ProductLog[(0.003*Sqrt[6])/Abs[(Sqrt[3]*Sin[\[Theta]]*Cos[\[Phi]])/(2*Sqrt[Pi])]], {\[Theta], 0, Pi}, {\[Phi], 0, 2*Pi}]

and end up with this

This appears to be the same as the question you asked here: Unknown plotting issue . Better to add to, expand, or clarify your original question than to start a new one. — Jagra, Feb 09 '21 at 20:21

Jagra · Answer 1 · 2021-02-09T21:23:37.230

Extended comment.

Just suggestions so that you can (maybe) see what you actually plot vs what you want to plot:

Plot3D[-2*
  ProductLog[(0.003*Sqrt[6])/
    Abs[(Sqrt[3]*Sin[\[Theta]]*Cos[\[Phi]])/(2*Sqrt[Pi])]],
 {\[Theta], 0, Pi},
 {\[Phi], 0, 2*Pi}, PlotRange -> All,
 ImageSize -> 500]

or...

SphericalPlot3D[-2*
  ProductLog[(0.003*Sqrt[6])/
    Abs[(Sqrt[3]*Sin[\[Theta]]*Cos[\[Phi]])/(2*Sqrt[Pi])]],
 {\[Theta], 0, Pi},
 {\[Phi], 0, 2*Pi},
 PlotRange -> All,
 ImageSize -> 500]

SphericalPlot3D generates flat surfaces

1 Answers1