On the energy spectrum of the one-dimensional Klein-Gordon Oscillator

TL;DR

This paper introduces a method to incorporate harmonic potential into the Klein-Gordon equation, resulting in explicit solutions for bound states, eigenfunctions, and eigenenergies in a one-dimensional setting.

Contribution

It presents a novel approach to modeling the Klein-Gordon oscillator with explicit solutions for bound states and energy spectra.

Findings

Explicit eigenfunctions derived

Eigenenergies calculated

Bound states established

Abstract

In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.