Functional Representation of the Wave Operator

摘要

Considerable simplification in the algebraic formalism of quantumhyphen;mechanical perturbation theory is achieved by representing the wave operator by a function PSgr; / (Npsgr;0). The differential equation for the wave operator is derived and used to generate Rayleighmdash;Schrouml;dinger perturbation theory. The Louml;wdin 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 zerothhyphen;order HamiltonianH0so that the wavefunction, accurate through the first order of perturbation, is equal to the exact wavefunction, or the wave operator times the reference function.