PH3203 - Lecture 5a

I discuss degenerate perturbation theory in this lecture. I first recapitulate the basic ideas of Rayleigh-Schrodinger perturbation theory, that we had looked at in detail in earlier lectures. I then go on to address the major issue that ensues when the energy level on which the effect of perturbation is being investigated happens to be degenerate - which is that the zeroth order equation can no longer specify the unperturbed wave function. This is remedied by looking at the first order perturbation equation, which leads to a matrix eigenvalue equation. The eigenvalues yield the first order energy corrections - which may, at least partially, lift the original degeneracy. Not only that, the eigenvectors of this matrix tells us which precise combinations of the degenerate unperturbed eigenfunctions provide zeroth order solutions from which we should start. I then go on to talk about higher order perturbation theory with specific reference to the changes that need to be made for the degenerate case.