Functional Representation of the Wave Operator

Abstract

Considerable simplification in the algebraic formalism of quantum-mechanical perturbation theory is achieved by representing the wave operator by a function Ψ / (Nψ0). The differential equation for the wave operator is derived and used to generate Rayleigh—Schrödinger perturbation theory. The Löwdin bracketing theorem is derived without the use of formal algebra and discussed in the context of perturbation theory. It is shown that nonlocal potential terms can be introduced into the zeroth-order Hamiltonian H0 so that the wavefunction, accurate through the first order of perturbation, is equal to the exact wavefunction, or the wave operator times the reference function.