The noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field

TL;DR

This paper explores the bound states and energy spectrum of a noncommutative Dirac oscillator with an electric dipole in an electromagnetic field, revealing how noncommutativity and external fields influence relativistic quantum systems.

Contribution

It provides new analytical solutions for the noncommutative Dirac oscillator with electric dipole moments under electromagnetic fields, generalizing previous models and analyzing spectrum features and degeneracies.

Findings

Spectrum depends linearly on potential energy and quantum numbers.

Degeneracy and behavior of the spectrum are analyzed graphically.

Results include the nonrelativistic limit and generalize previous literature.

Abstract

In this paper, we investigate the bound-state solutions of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in (2+1)-dimensions. We consider a radial magnetic field generated by anti-Helmholtz coils, and the uniform electric field of the Stark effect. Next, we determine the bound-state solutions of the system, given by the two-component Dirac spinor and the relativistic energy spectrum. We note that this spinor is written in terms of the generalized Laguerre polynomials, and this spectrum is a linear function on the potential energy $U$, and depends explicitly on the quantum numbers $n$ and $m$, spin parameter $s$, and of four angular frequencies: $\omega$, $\tilde{\omega}$, $\omega_\theta$, and $\omega_\eta$, where $\omega$ is the frequency of the oscillator, $\tilde{\omega}$ is a type of ``cyclotron frequency'', and $\omega_\theta$ and $\omega_\eta$ are the noncommutative frequencies of position and momentum. Besides, we discussed some interesting features of such a spectrum, for example, its degeneracy, and then we graphically analyze the behavior of the spectrum as a function of the four frequencies for three different values of $n$, with and without the influence of $U$. Finally, we also analyze in detail the nonrelativistic limit of our results, and comparing our problem with other works, where we verified that our results generalize several particular cases of the literature.