Exact Eigenvalues and Eigenfunctions of the Hulthen Potential in the PT-Symmetry for Any Angular Momentum

TL;DR

This paper provides an exact analytical solution for the eigenvalues and eigenfunctions of the PT-symmetric Hulthen potential, including the effects of angular momentum, using the Nikiforov-Uvarov method.

Contribution

It offers a novel exact solution for the Hulthen potential in PT-symmetry for any angular momentum state, extending previous numerical results.

Findings

Eigenfunctions expressed in Jacobi polynomials

Numerical results agree with prior studies

Analytical solutions for all angular momentum states

Abstract

The Schrodinger equation with the PT-symmetric Hulthen potential is solved exactly by taking into account effect of the centrifugal barrier for any l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. Our numerical results are in good agreement with the ones obtained before. Keywords: Energy Eigenvalues and Eigenfunctions; Hulthen potential; PT-symmetry; Nikiforov-Uvarov Method.