Solution of the D-dimensional Klein-Gordon equation with equal scalar and vector ring-shaped pseudoharmonic potential

TL;DR

This paper provides an exact analytical solution to the D-dimensional Klein-Gordon equation with a noncentral ring-shaped pseudoharmonic potential, deriving energy levels and eigenfunctions for spin-zero particles using the Nikiforov-Uvarov method.

Contribution

It introduces a novel exact solution for the Klein-Gordon equation with a noncentral potential in arbitrary dimensions, extending previous three-dimensional results.

Findings

Derived explicit bound-state energy levels

Obtained eigenfunctions for the potential

Reduced solution to known 3D case when coupling is zero

Abstract

We present the exact solution of the Klein-Gordon equation in D-dimensions in the presence of the noncentral equal scalar and vector pseudoharmonic potential plus the new ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound-state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this noncentral ring-shaped pseudoharmonic potential can be reduced to the three-dimensional pseudoharmonic solution once the coupling constant of the noncentral part of the potential becomes zero.