Origin in Inertial Frame for Spin-Orbit Coupling?

[nonequilibrium]

Hello,

I've seen spin orbit coupling being explained by going to the rest frame of the electron and noting that the proton is then a moving charge and hence has a magnetic field, which interacts with the spin of the electron, effectively coupling the spin and angular momentum of the electron.

What is the physical origin as seen from the inertial reference frame? If I would have to take a guess: the electron has an intrinsic magnetic field, and if it is orbiting, this magnetic field is changing in time, and hence induces an electric field, which interacts with the proton, so this changes the Hamiltonian with a term that should depend on L and S (of the electron).

 

[azntoon]

Is this correct? How does the angular momentum of the electron come into play?The physical origin of spin-orbit coupling can be explained from both inertial and non-inertial frames. In the inertial frame, spin-orbit coupling is caused by the relativistic effects of the electric and magnetic fields produced by the motion of the electron in the presence of a proton. The electric field exerts a force on the electron, causing it to move in a circular trajectory relative to the proton. This motion produces a magnetic field that interacts with the electron's intrinsic spin, causing it to couple its spin and orbital angular momentum (L). The interaction between the magnetic field and the electron's spin causes a change in the energy of the system. This change is proportional to the magnitude of the electron's spin and its orbital angular momentum, and is known as the spin-orbit coupling term. The spin-orbit coupling term is responsible for the splitting of the energy levels of an atom in an external magnetic field. Hope this helps.Regards