Effective-mass Klein-Gordon Equation for non-PT/non-Hermitian Generalized Morse Potential

TL;DR

This paper solves the one-dimensional effective-mass Klein-Gordon equation for a non-PT-symmetric, non-Hermitian generalized Morse potential, deriving energy eigenvalues and eigenfunctions for both position-dependent and constant mass scenarios.

Contribution

It introduces a series expansion method to solve the Klein-Gordon equation with a non-Hermitian potential, providing explicit energy and wave function solutions.

Findings

Energy eigenvalues are obtained for the generalized Morse potential.

Eigenfunctions are explicitly derived for both variable and constant mass cases.

The method applies to non-Hermitian, non-PT-symmetric potentials.

Abstract

The one-dimensional effective-mass Klein-Gordon equation for the real, and non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the corresponding eigenfunctions are obtained. They are also calculated for the constant mass case.