Perturbation theory is used for problems which are too difficult.
. Assume H is dividable into a solvable part:
with
and
Example: Helium The last term is
, the other terms are just the
solution for the hydrogen twice in a tensor product. Solution of
,
. Then
.
In matrix language: so
. Unfortunately, this is not easily solvable.
Method: start with one and see how it changes as
is turned on.
for
very small.
Theory developed in perturbation expansion.