L3.4 Degeneracy resolved to second order (continued)
PROFESSOR: It's not unsuspected, because in some sense, energy eigenvalues, what you need, the first order energy's then split the state. The hope is that the second order energy split the states, so that's why you have to go to second order. So going to second order is something we had to do. There was no hope to do this before we go to second order. So let's go to second order, and order lambda squared. And we put n0l state in. The left hand side, happily, is 0. So we have n0l from the right hand side, en1 minus delta h psi 1. But again, psi 1 has two pieces, a piece in the space we had that we just calculated plus a piece in the space of v tilde n and 1 minus delta h psi 1 vn plus the energy, which would be en2 in here. And we hit with n0l, so we pick an al0. OK, that doesn't look that terrible. I don't know if you agree, but it really doesn't. Especially because a few things are gone. This term is zero. Why? Because state in the degenerate ...