Question: What is the reason for spin-orbit interaction without just assuming that the electron moves on a circular path around a nucleus?
Every explanation for spin-orbit coupling that I have read uses the semi-classical approach of the electron moving on circular trajectories (around the nucleus in the case of hydrogen). I am looking for an explanation from a purely quantum mechanical, or even better from a purely quantum field theoretical, point of view.
My problem is that the circular paths are something that has always just been justified by saying that on a larger scale everything has to look classical. If there is a mathematical proof for the validity of the circular path assumption, that would be fine for me, too. I only don't want to "just assume" the circular trajectories.