On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the Harmonic Oscillator

TL;DR

This paper investigates how Lorentz symmetry breaking induces a Coulomb-like potential affecting bound states of a nonrelativistic spin-half particle and explores its impact on a 2D harmonic oscillator.

Contribution

It introduces a novel scenario of Lorentz symmetry breaking effects on quantum systems with a fixed space-like vector field and analyzes their influence on bound states and harmonic oscillators.

Findings

Bound states are obtained for the particle under the Lorentz-violating potential.

The Coulomb-like potential significantly alters the energy spectrum of the harmonic oscillator.

The study provides new insights into Lorentz symmetry violation effects in nonrelativistic quantum systems.

Abstract

In this work, we obtain bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present a new possible scenario of studying the Lorentz symmetry breaking effects on a nonrelativistic quantum system defined by a fixed space-like vector field parallel to the radial direction interacting with a uniform magnetic field along the z-axis. Furthermore, we also discuss the influence of a Coulomb-like potential induced by Lorentz symmetry violation effects on the two-dimensional harmonic oscillator.