On a Modified Klein Gordon Equation

TL;DR

This paper introduces a modified Klein-Gordon equation relevant at ultra high energies, revealing solutions that resemble harmonic oscillator energy levels in the context of quark confinement.

Contribution

It presents a novel modification of the Klein-Gordon equation and demonstrates its solutions mimic harmonic oscillator levels for linear potentials.

Findings

Solutions resemble harmonic oscillator energy levels

Equation similar to beam equation derived

Applicable to quark confinement scenarios

Abstract

We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get solutions that mimic the Harmonic oscillator energy levels, surprisingly. An equation similar to the beam equation is obtained in the process.