Stationary perturbation theory without sums over intermediate states: Supersymmetric Expansion Algorithm

Abstract

In this work we show that results of Rayleigh-Schr\"{o}dinger perturbation theory can be easily obtained using the recently proposed supersymmetric expansion algorithm. Our formalism avoids the sums over intermediate states and yield directly corrections to the energy and eigenstates in terms of integrals weighted by the probability densities for the edge states of the involved supersymmetric Hamiltonians.