An improved approximation scheme for the centrifugal term and the Hulthen potential

TL;DR

This paper introduces a new approximation method for the centrifugal term in the Schrödinger equation with the Hulthen potential, providing accurate analytical solutions for bound states across arbitrary angular momentum states.

Contribution

A novel, systematic approximation scheme for the centrifugal term enabling analytical solutions for the Hulthen potential in quantum mechanics.

Findings

High agreement of energy eigenvalues with numerical methods

Analytical solutions for s-wave binding energies and eigenfunctions

The approximation scheme is accurate and systematically applicable

Abstract

We present a new approximation scheme for the centrifugal term to solve the Schrodinger equation with the Hulthen potential for any arbitrary l state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s-wave (l=0) analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.