On the Time-Independent Perturbation Theory

Abstract

Abstract The time-independent perturbation theory is developed for an arbitrary operator which can be expanded in powers of the perturbation parameter λ. A unified formulation allows the establishment of a formal interrelation between the methods of Rayleigh-Schrödinger and of Bril­ louin-Wigner. We introduce a nonunitary transformation operator to connect the nth eigenket of Ĥ(0) with the nth eigenket of Ĥ(λ) and it is proven that this operator satisfies a Lippmann-Schwinger type equation. A perturbation method based on this equation is proposed, and it is applied to describe an electron moving in a Yukawa potential.