# A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

## TL;DR

This paper investigates how Lorentz symmetry violation, modeled by a tensor background, influences the behavior of a relativistic quantum oscillator with Coulomb-type and linear scalar potentials, providing analytical solutions to the Klein-Gordon equation.

## Contribution

It introduces a novel analysis of a relativistic quantum oscillator affected by Lorentz symmetry violation, deriving analytical solutions under Coulomb-type and linear scalar potentials.

## Key findings

- Analytical solutions to the Klein-Gordon equation were obtained.
- Lorentz symmetry violation modifies the oscillator's behavior.
- The study extends understanding of quantum systems under Lorentz-violating backgrounds.

## Abstract

We consider a background of the violation of the Lorentz symmetry determined by the tensor $\left( K_{F}\right)_{\mu\nu\alpha\beta}$ which governs the Lorentz symmetry violation out of the Standard Model Extension, where this background gives rise to a Coulomb-type potential, and then, we analyse its effects on a relativistic quantum oscillator. Furthermore, we analyse the behaviour of the relativistic quantum oscillator under the influence of a linear scalar potential and this background of the Lorentz symmetry violation. We show in both cases that analytical solutions to the Klein-Gordon equation can be achieved.