Naive picture of understanding Spin-Orbit Coupling

[sokrates]

I was trying to explain the origin of spin-orbit coupling to a beginning student and I used the following naive analogy:

An electron orbiting around the nucleus "sees" the nucleus rotating about itself (the electron) in its own (electron's) reference frame, thus this is like a current loop about the electron and this "current loop" causes an effective magnetic field from the electron's perspective.

I kind of can see why this is not exactly correct (because of the classical references it makes), but could this at least be an intuitive view of understanding it?

I know spin-orbit coupling can be rigorously derived from relativistic QM (Dirac eq.) but I usually use the Schrödinger equation with a few higher order perturbative terms such as Rashba and Dresselhaus couplings...

It's been a while since I looked at special relativity so I might be making a serious conceptual error in my simple analogy, any ideas?

 

[olgranpappy]

I was trying to explain the origin of spin-orbit coupling to a beginning student and I used the following naive analogy:

An electron orbiting around the nucleus "sees" the nucleus rotating about itself in its own reference frame, thus this is like a current loop about the electron and this "current loop" causes an effective magnetic field from the electron's perspective.

I kind of can see why this is not exactly correct (because of the classical references it makes), but could this at least be an intuitive view of understanding it?

I know spin-orbit coupling can be rigorously derived from relativistic QM (Dirac eq.) but I usually use the Schrödinger equation with a few higher order perturbative terms such as Rashba and Dresselhaus couplings...

It's been a while since I looked at special relativity so I might be making a serious conceptual error in my simple analogy, any ideas?

yes. you will miss a factor of 1/2 called the Thomas correction... or Thomas precession.
http://en.wikipedia.org/wiki/Thomas_precession

 

[alxm]

Looks okay, except I got confused where you wrote 'nucleus rotating about itself' and thought first you were making an analogy of nuclear spin (which isn't involved). You must've meant the electron as 'itself'.

AFAIK, your analogy is how it's usually rationalized. Looking in the few textbooks I have around, I can't find any examples of them not using a similar analogy. There is an error, which is that it's a rotating frame of reference, which raises some SR warning flags. You naturally need the whole relativistic calculation to do it all correctly, but since there's quite some learning to be done between first learning of spin-orbit coupling and learning to do relativistic QM calculations, I don't think it'd be worth going into, apart from mentioning.

 

[sokrates]

Right, I tried to say the nucleus rotating about the electron, itself...

It's good to know it's commonly rationalized this way, now I have an intuitive way of predicting why spin-orbit coupling is more observable in HEAVIER atoms than lighter atoms (nuclei)... It's like turning up the current in the current loop (more protons are revolving around the electron) and making the induced B-field stronger.

Thanks for the comments and insights axlm, and olgranpappy.