PH3203 : Lecture 11

In this lecture I describe a few applications of the WKB method. After a quick recapitulations of the basic ideas, I first use the Bohr-Sommerfeld quantization conditions to discuss the harmonic oscillator. The WKB method returns the exact result for the energy eigenvalues of this system. I then demonstrate how the WKB wavefunctions compare with the exact ones. I also discuss the quartic oscillator and determine an approximate formula for its energy eigenvalues. I next examine the situation where a potential is defined only for half of the real line and indicate how this can be used to solve the problem of central potentials in 3D. I end this lecture by using the Bohr-Sommerfeld principle to estimate the change in energy due to a perturbation and compare this with the result from Rayleigh-Schrodinger theory.