Large Perturbation Method

TL;DR

This paper introduces a novel numerical approach for solving eigenstate problems using perturbation theory reformulated as differential equations, offering advantages in speed and insight over traditional methods.

Contribution

It presents a new numerical method based on first order perturbation theory reformulated as differential equations, applicable to eigenvalue problems like the Schrödinger equation.

Findings

Faster than conventional variational methods in some cases

Allows perturbation terms of any magnitude

Provides new insights into perturbation theory

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.