We compute the energy change due to a weak magnetic field using first order Perturbation Theory.
The is harder since we are not in eigenstates of that one. We need , but we don't know how acts on these. So, we must write in terms of .
We already know how to write in terms of these states of definite and .
Let's do the state first.
So adding this to the (easier) part above, we have
In summary then, we
rewrite the fine structure shift.
Jim Branson 2013-04-22