An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

TL;DR

This paper enhances the asymptotic iteration method for solving exactly solvable eigenvalue problems by deriving a simplified formula and establishing a connection with the Nikiforov-Uvarov method, improving analytical solutions.

Contribution

The paper introduces a simplified formula for the asymptotic iteration method and links it to the Nikiforov-Uvarov method, advancing analytical solution techniques for eigenvalue problems.

Findings

Derived a simplified formula for the asymptotic iteration method.

Established a connection between the asymptotic iteration and Nikiforov-Uvarov methods.

Improved analytical solutions for exactly solvable eigenvalue problems.

Abstract

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov--Uvarov methods, which both solve the second order linear ordinary differential equations analytically.