[QE-users] Interpretting projwfc.x output

[Johnson, Miles R.]

Hi all,

I'm trying to interpret the m labels in the output files.

For collinear, spin-unpolarized, the projected dos is written PDOS_m. I would like to confirm that the m here labels real spherical harmonics  https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics

In other words, the ordering is linear combinations of the complex spherical harmonics https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Complex_Spherical_harmonics such that the ordering of the phi dependence is 1,cos(phi), sin(phi),cos(2phi),sin(2phi)...

This interpretation remains true including spin-orbit coupling, except that m refers to m_j and the wavefunctions are eigenstates of J_z=L_z+S_z and J^2 as per standard addition of angular momentum.

It's taken a little while for me to settle on this interpretation so just trying to confirm that I'm correct. Please let me know!

Thanks,
Miles Johnson
Applied Physics Phd Candidate
California Institute of Technology

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20221117/662b0af8/attachment.html>