Analytic l-state solutions of the Klein-Gordon equation for q-deformed Woods-Saxon plus generalized ring shape potential

TL;DR

This paper derives analytical solutions for the Klein-Gordon equation with a q-deformed Woods-Saxon plus generalized ring shape potential, providing eigenvalues and eigenvectors in closed form using the asymptotic iteration method.

Contribution

It introduces a novel analytical approach to solve the Klein-Gordon equation with a q-deformed potential and generalizes previous solutions for specific cases.

Findings

Eigenvalues expressed in closed form

Eigenvectors formulated with generalized Jacobi and Legendre polynomials

Solutions recover known results for standard Woods-Saxon potential

Abstract

The analytical expressions for the eigenvalues and eigenvectors of the Klein-Gordon equation for q-deformed Woods-Saxon plus new generalized ring shape potential are derived within the asymptotic iteration method. The obtained eigenvalues are given in a closed form and the corresponding normalized eigenvectors, for any l, are formulated in terms of the generalized Jacobi polynomials for the radial part of the Klein-Gordon equation and associated Legendre polynomials for its angular one. When the shape deformation is canceled, we recover the same solutions previously obtained by the Nikiforov-Uvarov method for the standard spherical Woods-Saxon potential. It is also shown that, from the obtained results, we can derive the solutions of this problem for Hulthen potential.