Any $l$-state solutions of the Hulth\'en potential by the asymptotic iteration method

TL;DR

This paper analytically solves the radial Schrödinger equation for the Hulthén potential using the asymptotic iteration method, providing energy eigenvalues and eigenfunctions that agree with other established methods across various screening parameters.

Contribution

It introduces an analytical solution for all $l$ states of the Hulthén potential using the asymptotic iteration method with an approximation for the centrifugal potential.

Findings

Energy eigenvalues match other methods for different $elta$ values.

Wave functions are physically acceptable.

Results are consistent with supersymmetry, numerical, variational, and shifted 1/N methods.

Abstract

In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta $ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.