I'll start off by going back to the Two-State Problem. After attempting the homework problem on this, it makes a bit more sense, but not a lot. Basically Sakurai does perturbation using matrices. It still doesn't help me with the homework, though. Next Sakurai formally develops perturbation theory. He shows how to calculate the first order shift in the energy and the wavefunction. He then briefly does the higher orders. Next he renormalizes the wave-function, but I didn't understand this section at all. Basically, I don't understand Sakurai sometimes. This whole section is particularly dense. Then there are two examples.
I don't think I'll devote another post to the next section, which involves the degenerate case. Basically, you need to diagonalize the perturbation matrix. Only then will the degeneracy lift and you can solve the problem as in the non-degenerate case.
I think I will have to supplement with Townsend, discussion section, and banging through the homework as best I can. There is also Baym. Onward and upward.
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