###

Hydrogen in a Strong B Field

We need to compute the matrix elements of the hyperfine perturbation
using
as a basis with energies
.
The perturbation is

where
.
Recalling that we can write

the matrix elements can be easily computed.
Note that the terms like
which change the state will give zero.

We can write all of these in one simple formula that only depends on relative sign of
and
.

Jim Branson
2013-04-22