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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