Spin-Orbit Coupling: A Bohr-Orbital Model?

[Fightfish]

In most introductory discussions on spin-orbit coupling in the hydrogen atom that I've come across, the analysis is often performed on a Bohr-orbital model. The electron is treated as orbiting the nucleus in a circular orbit. They then transform to the frame of the electron, and then assert that the orbital motion can be analyzed as a current loop.

But I cannot help but question the validity of such a model. While admittedly the semiclassical Bohr model is able to make some rather accurate predictions of some physical parameters, this particular case feels kind of stretched to me.

Could someone perhaps assist me in clearing this doubt up? Thanks.

 

[Bill_K]

Fightfish, I agree with you - this approach to the derivation of spin-orbit coupling is highly questionable. Take a look at the quantum book by Schiff, which does it right! The derivation makes use of the Dirac equation, of course, but is only a single page long (page 482 in the edition I have).

 

[DrDu]

In a hydrogen atom, at least in the ground state, L=0 so there should be no SO coupling. This is also clear classically as the Bohr Sommerfeld orbits are lines which pass through the nucleus. Circular orbits would correspond to states with very high values of L (so called Rydberg states). For these states a semiclassical analysis should be correct. Such a semi-classical analysis may help to get some intuition on how to interprete the different terms in the Dirac equation.