Second-order corrections to the non-commutative Klein-Gordon equation with a Coulomb potential

TL;DR

This paper advances the understanding of the non-commutative Klein-Gordon equation by calculating second-order corrections, revealing non-commutativity as a source of Lamb shift effects in the hydrogen atom.

Contribution

It introduces second-order non-commutative corrections to the Klein-Gordon equation for the hydrogen atom, providing a more precise theoretical framework.

Findings

Non-commutativity causes measurable Lamb shift corrections.

Second-order corrections refine energy level predictions.

Non-commutative effects could be experimentally detectable.

Abstract

We improve the previous study of the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity parameter. Phenomenologically we show that non-commutativity is the source of lamb shift corrections.