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

TL;DR

This paper introduces a supersymmetric expansion algorithm that simplifies stationary perturbation theory by eliminating the need for sums over intermediate states, providing direct energy and eigenstate corrections.

Contribution

The work presents a novel supersymmetric expansion method that streamlines perturbation calculations without summing over intermediate states.

Findings

Efficient calculation of energy corrections using supersymmetric formalism

Direct determination of eigenstate corrections via integrals

Simplification of Rayleigh-Schrödinger perturbation theory

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.