Spin-Orbit Interaction and its effect of the degeneracy manifolds of hydrogen

The spin-orbit interaction is, at its heart, an interaction between an electron and a proton. However, it is different from the coulomb interaction, $-e^2/r$, in that it depends on the orientation of the spin? What does that mean? What are its consequences? etc. etc.

Those are hard questions. In a way, this is a preview of things that will be covered in Physics 139. One key consequence is that it changes the energies of the states a little bit, of order $10^{-4}$ eV. Equally or more important, it changes the fundamental structure and nature of the degeneracies. Instead of an eightfold degenerate 1st-excited state, one ends up with 6 and 2-fold degeneracies. The eigenstates are specific linear combinations of our "original" eigenstates.

If you get to the end of this and want to see more, maybe post a comment. That will give me some motivation to continue the story.

Here are two more pages. Please feel free to continue the discussion her or in the comments of the HW9 post.