Projection operator approach to time-independent perturbation theory in quantum mechanics

Abstract

The time-independent perturbation theory in quantum mechanics is formulated using projection operator techniques. The determination of the perturbed eigenvalue can be decoupled from that of the perturbed eigenstate. Both the Brillouin–Wigner theory and the Rayleigh–Schrödinger theory come out straightforwardly. Both degenerate and nondegenerate cases can be treated in a unified way for arbitrarily high order perturbations.