In second order, you get: . numerator not 0 for l=1 and n
1.
Approximation gives:
= quadratic stark effect. Polarization=
. Polarizability=
polarization.
This is
. Actual calculation gives
which agrees well with experimentation.
For excited states:
For n=2, there is 8 fold degeneracy
With spin orbit coupling, you get a 6 fold degeneracy on .
Weak fileds - non-degenerate P.T. =
2nd order quadratic.
Strong fields, then 2s and 2p are degenerate.
. Constructing a 4x4 matrix, you get:
. Diagonilizing, you get: the roots, 0,0,
. The eigen states are
,
. This is the linear stark effect. Only shows up for strong fields,
when lamb shifts and spin orbit coupling are neglectable. This means
.