Effects of Lorentz Symmetry Breaking Environment on Generalized Relativistic Quantum Oscillator Field

TL;DR

This paper investigates how Lorentz symmetry breaking influences the solutions of the generalized Klein-Gordon oscillator, revealing modifications to eigenvalues in the presence of Lorentz-violating tensor fields and external electromagnetic fields.

Contribution

It introduces a novel analysis of the relativistic quantum oscillator under Lorentz symmetry violation using the Nikiforov-Uvarov method with Coulomb and Cornell potentials.

Findings

Eigenvalues are modified by Lorentz-violating effects.

External electric and magnetic fields influence the quantum states.

The study extends understanding of Lorentz symmetry breaking in quantum oscillators.

Abstract

In this paper, we study the generalized Klein-Gordon oscillator equation under the effects of the violation of Lorentz Symmetry defined by a tensor field $(K_F)_{\mu\nu\alpha\beta}$ out of the Standard Model Extension (SME). We consider a possible scenario of the Lorentz-Violating effects with a Cornell-type electric field and a linear magnetic field that contributes a harmonic-type central potential in the relativistic quantum motions of scalar oscillator fields. The bound-states solutions of the wave equation using the parametric Nikiforov-Uvarov method by considering a Coulomb and Cornell-type potential form functions are obtained. We see that the eigenvalue solutions get modified by the Lorentz symmetry-breaking effects in comparison to the Landau levels (without Lorentz-Violation effects in flat space)