PH3203 - Lecture 4

In this lecture I continue with non-degenerate perturbation theory. To begin, I show how you can use the equations for RSPT that we had derived in the last lecture to determine corrections to the ground state energy and wavefunction of a harmonic oscillator with a quartic anharmonicity. I then go on to derive a relatively less well known, but useful formula - the 2s +1 rule, which shows us how the determine the 2s+1 order energy correction from just the knowledge of wavefunction and energy corrections up to order s (conventional RSPT only allows you to find the energy correction of order s+1 from this information). I finish by using this to calculate the energy correction to the third order for the ground state of the anharmonic oscillator, using the first order energy and wave function corrections.