Relation of Perturbation Theory to Variation Method

Abstract

The various order wave functions of the Rayleigh‐Schrödinger perturbation theory can be obtained directly by solving certain differential equations or by minimizing equivalent variational expressions. These expressions are related to the ordinary variation method. The perturbation series is shown to result in a unique way from the minimization of larger and larger portions of 〈ψ, Hψ〉/〈ψ, ψ〉. In addition to several orders of perturbation, each step gives the exact remainders and upper limits to the energy. The approach suggests several ``variation‐perturbation'' schemes.