Approximate Analytical Solutions of the Effective Mass Klein-Gordon Equation for Two Interacting Potentials

O Ebomwonyi ,Atachegbe Clement Onate,Joshua O Okoro ,M C Onyeaju ,Matthew Olanrewaju Oluwayemi

doi:10.4038/sljp.v19i1.8042

Abstract

In this study, the approximate analytical solutions of the relativistic Klein-Gordon equation in the spatial dimensions with unequal Coulomb-inverse Trigonometry scarf scalar and vector potentials for an effective mass function is investigated in the framework of supersymmetric and shape invariance method by employing a suitable approximation scheme to the centrifugal term. The energy equation for some special cases such as the Coulomb potential and inverse Trigonometry scarf potential are obtained. Using a certain transformation, the non-relativistic energy equation is obtained which is identical to the energy equation of the Hellmann potential.

Highlights

In the recent years, the analytical approximate methods to the relativistic wave equation such as Dirac equation and Klein-Gordon equation have attracted a great number of interest in Physics[1]
The purpose of this study is to investigate the spatial dimensions of the Klein-Gordon equation with a combination of Coulomb potential and inverse Trigonometric scarf potential with unequal vector and scalar potential for an effective mass function
In this work, we critically examined the Klein-Gordon equation with unequal scalar and vector potentials using supersymmetric approach

Summary

INTRODUCTION

The analytical approximate methods to the relativistic wave equation such as Dirac equation and Klein-Gordon equation have attracted a great number of interest in Physics[1]. A great number of studies have been devoted to obtain the analytic solutions of the relativistic Klein equation with the well-known potentials such as Woods-. It is understood that the exact solutions of the Klein-Gordon equation are only possible for some physical potential types. N-dimensional space of the Klein-Gordon equation with a combination of Coulomb potential and inverse Trigonometry scarf potential. The purpose of this study is to investigate the spatial dimensions of the Klein-Gordon equation with a combination of Coulomb potential and inverse Trigonometric scarf potential with unequal vector and scalar potential for an effective mass function. Where and B are the potential parameters and r is the inter nuclear separation

BOUND STATE SOLUTION

Special cases