Large Perturbation Method

Abstract

This paper describes a new numerical method for solving eigenstate problems, such as time-independent Schrodinger equation. The idea is to use the first order perturbation theory to rewrite the eigenvalue problem as a system of first order differential equations and then solve them using numerical techniques. The method allows to introduce perturbation terms of any order of magnitude. The algorithm is in some cases faster than conventional variational method and offers a new insight into perturbation theory. It is also easy to understand and implement.