Then we compute the energy shift in first order perturbation theory for s states.
The second term can be simplified because of the spherical symmetry of s states.
(Basically the derivative with respect to x is odd in x so when the integral is done,
only the terms where
So we have
Now working out the
term in spherical coordinates,
To find the effect at
we will integrate.
Simply writing the
in terms of
and regrouping, we get
We will sometimes group the constants such that
(The textbook has numerous mistakes in this section.)
Jim Branson 2013-04-22