CHAPTER VI – PERTURBATION THEORY

Publisher Summary This chapter discusses perturbations independent of time. The exact solution of Schrodinger's equation can be found only in a comparatively small number of the simplest cases. The majority of problems in quantum mechanics lead to equations that are too complex to be solved exactly. Often, however, quantities of different orders of magnitude appear in the conditions of the problem; among them, there may be small quantities, such that when they are neglected, the problem is so much simplified that its exact solution becomes possible. In such cases, the first step in solving the physical problem concerned is to solve exactly the simplified problem, and the second step is to calculate approximately the errors as a result of the small terms that have been neglected in the simplified problem. There is a general method of calculating these errors; it is called perturbation theory. As a result of the perturbation, an originally degenerate energy level ceases to be degenerate. The perturbation removes the degeneracy. The removal of the degeneracy may be either total or partial.