# Recreate DensityMatrixPlot

asked by David Tam (2022/03/27 19:10)

In Mathematica, I define the basis according to the documentation for DensityMatrixPlot:

lbasisF = With[{l = 3}, Flatten[Table[{SphericalHarmonicY[l, m, \[Theta], \[Phi]], SphericalHarmonicY[l, m, \[Theta], \[Phi]]}, {m, -l, l}]]];

Now I can construct a density matrix with some randomly chosen numbers, and make a plot:

dmF = CFDensityMatrix[3, 1, With[{vv = {0.7, 0, 0.3, 0, 0, 0.3, 0, 0, 0.1, 0.5, 0.1, 0, 0.2, 0}}, vv/Sqrt@Total[vv^2]]]

DensityMatrixPlot[dmF]

However, the following superposition shows that directly plotting in the orbital basis doesn't make the same plot:

Show[ dmplot, SphericalPlot3D[ Conjugate[lbasisF].dmF.lbasisF, {\[Theta], 0, Pi}, {\[Phi], 0,(*2 Pi*)Pi} , PlotRange -> All, AspectRatio -> Automatic, AxesLabel -> {“x”, “y”, “z”}] ]

What is the right way to find the angular function as function of theta and phi, and how does DensityMatrixPlot avoid this problem?

## Answers

Hello David,

Which version of Mathematica are you using?

Dear David

There is a difference between the wave function $\sqrt{1/2} (p_x + p_y)$ and the charge density of the $p_x$ and $p_y$ orbital. I here used $p$ orbitals as they are simpler than the $f$ orbitals. Have a look at the tutorial at Quanty/tutorial/wavefunctions_and_density to see the difference.

You find this tutorial in the Mathematica Help files. Go to Help → Documentation → Add ons and packages (bottom) → Quanty → Documentation → Tutorials: Wave functions and density

This might solve your question Maurits