Application of Asymptotic Iteration Method (AIM) to a Deformed Well Problem

TL;DR

This paper applies the Asymptotic Iteration Method to solve the Schrödinger equation for a deformed well potential, revealing quasi-exact solutions and deriving simple analytical expressions for energy eigenvalues.

Contribution

It introduces the AIM approach to a deformed well problem, providing analytical solutions and extending to general potential parameters.

Findings

Eigenvalues obtained for the deformed well potential

Quasi-exact solutions identified for the Schrödinger equation

Simple analytical expressions derived for energy eigenvalues

Abstract

We have used Asymptotic Iteration Method (AIM) for obtaining the eigenvalues of the Schrodinger's equation for a deformed well problem representing trigonometric functions. By solving the problem, we have found that the Schrodinger's equation for the considered potential has quasi-exact solutions. Additionally, we have also calculated the perturbation expansion of energy eigenvalues and found very simple analytical expression of the energy. Finally, we have considered more general cases and obtained energy eigenvalues for arbitrary potential parameters.