Perturbation theory in a framework of iteration methods

TL;DR

This paper extends the asymptotic iteration method to perturbed quantum mechanical problems, enabling direct calculation of eigenvalues and eigenfunctions without solving the unperturbed case first.

Contribution

It introduces a novel application of the asymptotic iteration method to perturbation theory in quantum mechanics, simplifying the computation process.

Findings

Direct computation of perturbation series coefficients

Application to quantum eigenvalue problems

Avoids solving unperturbed equations first

Abstract

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem.