Dirac Equation in Noncommutative Space for Hydrogen Atom

TL;DR

This paper investigates how space noncommutativity affects the energy levels of a hydrogen-like atom using a modified Dirac equation, revealing that degeneracies are lifted and new transition channels emerge.

Contribution

It introduces a noncommutative space framework to analyze hydrogen atom energy levels, showing complete lifting of degeneracies in the Dirac spectrum.

Findings

Degeneracy of 2S_{1/2}, 2P_{1/2}, 2P_{3/2} levels is fully lifted

New transition channels become possible due to noncommutativity

Noncommutative effects modify atomic energy spectra

Abstract

We consider the energy levels of a hydrogen-like atom in the framework of $\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels $2S_{1/2}, 2P_{1/2}$ and $ 2P_{3/2}$ is lifted completely, such that new transition channels are allowed.