Bound and scattering state of position dependent mass Klein-Gordon equation with Hulthen plus deformed-type hyperbolic potential

TL;DR

This paper analytically investigates bound and scattering states of the Klein-Gordon equation with a deformed Hulthen and hyperbolic potential in D-dimensions using supersymmetry and factorization methods, providing explicit eigenvalues and phase shifts.

Contribution

It introduces a novel analytical approach to solve the Klein-Gordon equation with complex potentials in arbitrary dimensions, deriving explicit eigenvalues and phase shifts.

Findings

Closed-form relativistic bound state eigenvalues

Analytic scattering phase factors

Numerical results for bound state energies in D-dimensions

Abstract

In this article we used supersymmetry quantum mechanics and factorization methods to study the bound and scattering state of Klein-Gordon equation with deformed Hulthen plus deformed hyperbolical potential for arbitrary state in D-dimensions. The analytic relativistic bound state eigenvalues and the scattering phase factor are found in closed form. We reported on the numerical results for the bound state energy in D-dimensions.