Perturbed Coulomb potentials in the Klein-Gordon equation via the shifted-1 expansion technique

TL;DR

This paper introduces a shifted-1 expansion technique to accurately compute energy eigenvalues for the Klein-Gordon equation with Coulomb-like potentials, including mixed Lorentz vector and scalar cases, demonstrating rapid convergence and exact solutions.

Contribution

A novel shifted-1 expansion method for Klein-Gordon equations with Coulomb-like potentials, providing accurate eigenvalues and closed-form solutions for specific potential configurations.

Findings

Exact eigenvalues for pure Lorentz vector/scalar Coulomb potentials.

Highly accurate ground-state energies for mixed potentials.

Closed-form solutions for specific Coulombic potentials.

Abstract

A shifted - l expansion technique is introduced to calculate the energy eigenvalues for Klein-Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that include Coulomb-like terms are only considered. Exact eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorenz scalar Coulombic potentials are reproduced. Highly accurate and rapidly converging ground-state energies for Lorentz vector Coulomb with a Lorentz scalar linear potential, V(r)=-A1/r+kr, and S(r)=kr, respectively, are obtained. Moreover, a simple straightforward closed-form solution for a KG-particle in a Coulombic Lorentz vector and Lorentz scalar potentials is presented in appendix A.