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.
For
,
So adding this to the (easier) part above, we have
for
.
In summary then, we
rewrite the fine structure shift.
Jim Branson 2013-04-22