L3.3 Degeneracy resolved to second order
PROFESSOR: We have a problem. The general perturbation theory, again, end states. But this time, the degeneracy is not broken. So degeneracy not lifted at first order. Surprisingly, this subject is, as you can see, you have to do things with care. It's not in any of the textbooks that I know. In fact, I don't know of any place where it is discussed in detail or discussed anywhere, even though this result is pretty useful and you need it, and I think people improvise when they do this. Even this discussion that with it here is not in any of your textbooks. In [INAUDIBLE],, the advanced quantum mechanics, there's some discussion and mentions this factor and how subtle it is, but doesn't quite do everything till the bitter end. This case is harder. This is simple compared to what we're going to do now. But we're going to sketch it so that you see the picture. We're going to do everything, but we're going to try to keep the picture clear becaus...