Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

TL;DR

This paper demonstrates how the asymptotic iteration method (AIM) can be used to construct exact solutions for a broad class of eigenvalue problems, including various quantum mechanical potentials and higher-dimensional cases.

Contribution

The paper extends the AIM to solve new classes of second-order linear differential equations, including generalized eigenvalue problems in higher dimensions.

Findings

Exact solutions for Schrödinger problems with Coulomb, harmonic oscillator, and Pöschl-Teller potentials.

Application of AIM to higher-dimensional eigenproblems.

Generalization of previous results to broader classes of differential equations.

Abstract

We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue problems which includes Schroedinger problems with Coulomb, harmonic oscillator, or Poeschl-Teller potentials, as well as the special eigenproblems studied recently by Bender et al [J. Phys. A: Math. Gen. 34 9835 (2001)] and generalized in the present paper to higher dimensions.