Approximation Methods for Stationary States

Abstract

Although we have succeeded in solving some important and interesting quantum mechanical problems, an exact solution is not possible in complicated situations, and we must then resort to approximation methods. For the calculation of stationary states and energy eigenvalues, these include perturbation theory, the variational method, and the WKB approximation. Perturbation theory is applicable if the problem differs from an exactly solvable problem by a small amount. The variational method is appropriate for the calculation of the ground state energy if one has a qualitative idea of the form of the wave function, and finally the WKB method is applicable in the nearly classical limit.