Dirac Equation under Modified Hylleraas Potential in Noncommutative Spaces

TL;DR

This paper investigates how noncommutative space modifies the Dirac equation with Hylleraas potential, revealing energy level splitting influenced by the noncommutation parameter and external electric fields.

Contribution

It introduces a first-order correction to the Dirac energy levels in noncommutative space with Hylleraas potential, highlighting the impact of the noncommutation parameter on energy splitting.

Findings

Noncommutation parameter causes energy level splitting.

Energy eigenvalues are significantly affected by noncommutativity.

Electric field induces slight numerical changes in energy levels.

Abstract

In this paper, we study the interaction of spin 1/2 Dirac particles with the Hylleraas potential based on the noncommutative space framework. Solving the first-order correction of the energy level caused by the noncommutation parameter $\theta$ in the wave equation. The problem of energy level correction under the action of additional weak electric field is further analyzed. Due to the non-commutation parameter, the energy levels are split. The noncommutation parameter $\theta$ has a significant effect on the energy eigenvalues. The effect of $\theta$ on the energy level splitting caused by the electric field is reflected by adding a slight numerical change to the energy level after splitting.