L2.3 Degenerate Perturbation theory Example and setup
PROFESSOR: OK, degenerate perturbation theory. OK, we've done nicely our non-degenerate case. So we'll get degenerate done in a very clear way, I think. One more blackboard. So the first thing I want to say about degenerate perturbation theories, when it fails and why it fails and what goes wrong. So degenerate perturbation theory. Trivial example to begin with, why not, h of lambda, again, is equal to h0 plus lambda delta h. And for h0, we'll take original Hamiltonian with energies 1 and 1, and for delta h, I'll take an off-diagonal Hamiltonian, a Pauli matrix, and that's our delta h. And then we say OK, blindly, not worry about this degeneracy, and use the formulas that we have for non-degenerate states. And we would say well, for the first state and the second state what do we have? E, I'll call them 1 and 2, not 0 and 1. So let's call them 1 of lambda will be equal to the first value, 1, plus, if the formula is right, delta h times lambda, ...