Perturbative calculation of energy levels for the Dirac equation with generalised momenta

TL;DR

This paper investigates how a noncommutative phase space modifies the Dirac equation, calculating perturbative corrections to energy levels for specific potentials, revealing potential significance of noncommutative effects.

Contribution

It introduces a perturbative method to compute energy level corrections in a noncommutative Dirac framework for linear potentials, extending standard quantum relativistic analysis.

Findings

Noncommutative contributions can be comparable to relativistic effects.

Lowest order energy corrections are explicitly calculated for two potentials.

Noncommutative structure influences eigenfunctions and energy spectra.

Abstract

We analyse a modified Dirac equation based on a noncommutative structure in phase space. The noncommutative structure induces generalised momenta and contributions to the energy levels of the standard Dirac equation. Using techniques of perturbation theory, we use this approach to find the lowest order corrections to the energy levels and eigenfunctions for two linear potentials in three dimensions, one with radial dependence and another with a triangular shape along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones.