Asymptotic Iteration method for singular potentials

TL;DR

The paper demonstrates the application of the asymptotic iteration method (AIM) to accurately compute eigenvalues for the radial Schrödinger equation with singular potentials, providing insights into convergence and stability improvements.

Contribution

It introduces a systematic application of AIM to singular potentials, discussing conditions for its use and proposing enhancements for convergence and stability.

Findings

AIM yields highly accurate eigenvalues for singular potentials.

The method is effective across all coupling ranges.

Convergence and stability improvements are proposed.

Abstract

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schroedinger equation with the singular potential V(r)=r^2+\lambda/r^\alpha (\alpha,\lambda> 0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials such as V(r) valid for all ranges of coupling \lambda.