### The Spin-Orbit Correction

We calculate the classical Hamiltonian for the spin-orbit interaction which we will later apply as a perturbation. The B field from the proton in the electron's rest frame is

Therefore the correction is

only depends on

Note that this was just a classical calculation which we will apply to quantum states later. It is correct for the EM forces, but, the electron is actually in a rotating system which gives an additional term (not from the B field!). This term is 1/2 the size and of opposite sign. We have already included this factor of 2 in the answer given above.

Recall that

and we will therefore want to work with states of definite , , and .

Jim Branson 2013-04-22