WKB ENERGY QUANTIZATION AND FIRST-ORDER PERTURBATION-THEORY

The WKB quantization condition can be used to estimate the quantized b ound state energies, E(n), in a potential V(x). If a small perturbatio n of the form lambda V'(x) is added to this potential, we show that th e resulting shift in the quantized energy eigenvalues is given by a fo rm which is quite similar to standard first-order perturbation theory. Several examples are presented in which the large n form of the lowes t-order energy shift is more easily evaluated using WKB-perturbation t echniques than by using standard first-order perturbation methods. (C) 1997 American Association of Physics Teachers.