### The Anomalous Zeeman Effect

We compute the energy change due to a weak magnetic field using first order Perturbation Theory.

The part is easy since we are in eigenstates of that operator.

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 ,

We can combine the two formulas for .

So adding this to the (easier) part above, we have

for .

In summary then, we rewrite the fine structure shift.

To this we add the anomalous Zeeman effect

Jim Branson 2013-04-22