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

2019/09/13 by Marco Maceda, Maceda, Marco, Jairo Villafuerte-Lara +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1909.06311

15 pages, 1 figure

arxiv created 2019/09/13 · openalex publication_date 2019/09/13 · arxiv updated 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Discreteness of Space from the Generalized Uncertainty Principle
• An introduction to the quark model
• Confinement potentials for the study of heavy mesons

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