QM: Spin-orbit and wavefunctions for H

[Niles]

Homework Statement

Hi all.

I wish to evaluate the following dipole moment

$$<1| x |2>,$$

where |1> and |2> are stationary states of the hydrogen atom when one accounts for spin-orbit coupling. I am a little unsure of if I am allowed to use the "normal" unperturbed wavefunctions for hydrogen in this case, or if the wavefunctions change because of spin-orbit?

 

[Matterwave]

I don't think so, the spin-orbit coupling will shift your energies, which means that the eigenstates have changed.

So |1> and |2> are not the same as the regular ones...I think you're going to have to calculate the perturbed wave functions.

 

[Niles]

This is what I feared.. it seems like a pretty long task.