Perturbation Theory

Abstract

The problem of finding the quantum levels of a system (i.e. of finding the eigenvalues and eigenfunctions of the energy operator H) can be solved by means of known mathematical functions in only a very few cases. In most problems of atomic mechanics such simple solutions do not exist. Considerable importance therefore attaches to a wide range of cases where the problem concerned can be approximately reduced to that of a simpler system for which the eigenvalues E ^o_n and eigenfunctions Ψ ^o_n are known. This possibility arises when the energy operator H of the system under consideration differs only slightly from the operator H^o of the simpler system.