At university we have just derived the expression for the energy split due to spin-orbit coupling in the Hydrogen atom, i.e. what is known as the FINE structure of Hydrogen.
To do this, we considered the situation from the frame of reference of the electron: in this frame, the proton is moving and therefore generates a magnetic field ( because it's a moving charged particle) which couples to the electron's spin.
What if I wanted to consider the situation in the nucleus' (proton's) frame of reference? The moving charged particle is the electron and it is generating a magnetic field (which as it happens couples to the spin of the nucleus and results in the hyperfine structure). But the magnetic field of the electron cannot couple to its own spin? Or can it? How do I explain the energy spit in this reference frame? Physics must be the same in all frames of reference right?