Change of basis
asked by Victor Porée (2026/04/21 11:05)
Hi,
I am looking for a way to express eigenstates from a list of inital/final XAS states (Cr 2p3d) on the basis of pure |J,jz> for the 2p and |L,S,lz,sz> for the 3d.
Best,
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Answers
Dear Victor,
You could calculate the eigenstates of the $L^2$, $L_z$, $S^2$ and $S_z$ or $J^2$ and $J_z$ operator and project to these. As you want simultaneous eigenstates you can define the operator $L^2 + 0.1 S^2 + 0.01 L_z + 0.001 S_z$ and calculate its eigenstates and eigenvalues.
For small systems this is instructive, for larger systems there are better ways to look at the spectrum.
Have a look at the partial spectra examples where we project the excitation operator to a given subspace.
Best wishes, Maurits