Do perturbation theory around a 0th order degenerate state.

Then

If partially splits the degeneracy, then the particular basis you choose in the degenerate subspace is important.

Define projectors:

, P is the projector of the degenerate subspace. In the degenerate subspace: .

Define , . Solving exactly is first order degenerate perturbation theory. Solving is second order.

Solutions of which are less degenerate... Then higher order approximations don't have to worry about degeneracy.

And

applications:

- explicitly construct gxg matrix and diagonalize
- coupling angular momentum via clebsch-gordon gives diagonal basis

source

psfile jl@crush.caltech.edu index

perturbation_theory

TDPT