Asymptotic iteration method for eigenvalue problems

TL;DR

This paper introduces an asymptotic iteration method for solving second-order linear differential equations, with applications to Schrödinger problems including those with singular potentials.

Contribution

The paper presents a novel asymptotic iteration technique specifically designed for second-order linear differential equations with applications to quantum mechanics.

Findings

Effective in solving Schrödinger equations with singular potentials

Demonstrates convergence and accuracy of the method

Applicable to a wide class of differential equations

Abstract

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.