Rotational and vibrational diatomic molecule in the Klein-Gordon equation with hyperbolic scalar and vector potentials

TL;DR

This paper provides an approximate analytical solution for the energy levels and wave functions of a spin-zero particle in a Klein-Gordon framework with hyperbolic potentials, using a generalized Nikiforov-Uvarov method.

Contribution

It introduces a novel parametric approach to solving the Klein-Gordon equation with hyperbolic potentials, deriving explicit bound state solutions.

Findings

Derived approximate energy levels and wave functions for the system.

Unified treatment of relativistic and non-relativistic cases.

Explicit solutions expressed in terms of Jacobi polynomials.

Abstract

We present an approximate analytic solution of the Klein-Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parameteric generalization of the Nikiforov-Uvarov method. We obtain the approximate bound state rotational-vibrational (ro-vibrational) energy levels and the corresponding normalized wave functions expressed in terms of the Jacobi polynomial for a spin-zero particle in a closed form. Special cases are studied including the non-relativistic solutions obtained by appropriate choice of parameters and also the s-wave solutions.