Effects of a linear central potential induced by the Lorentz symmetry violation on the Klein\u2013Gordon oscillator

R L L Vitória,H Belich

doi:10.1140/epjc/s10052-018-6479-4

Abstract

Inspired by the Standard Model Extension, we have investigated a possible scenario arising from the Lorentz symmetry violation governed by a background tensor field on a scalar field subject to the Klein–Gordon oscillator, where this possible scenario gives rise to a linear central potential. We analyse the behaviour of the relativistic quantum oscillator under the influence of a Coulomb-type scalar potential in this background. Then, we solve the Klein–Gordon equation analytically and discuss the influence of the background which violates the Lorentz symmetry in the relativistic energy levels.

Highlights

In recent years, in order to observe more accurately the atomic nuclei, some investigations, taken into account the hydrogen atom, have considered to change the orbital electron by a muon, and they have shown that the proton radius is little different [1]
Another quantum effect from the possible scenario of Lorentz symmetry violation (LSV) is that the angular frequency of the Klein–Gordon oscillator has restricted values determined by the quantum numbers of the system and the parameters associated with spacetime anisotropy, which allow us to obtain a polynomial solution to the biconfluent Heun series
The presence of this linear central potential induced by LSV modifies the energy profile of the system and the lower energy state is determined by the radial mode n = 1 instead of the quantum number n = 0

Summary

Introduction

In order to observe more accurately the atomic nuclei, some investigations, taken into account the hydrogen atom, have considered to change the orbital electron by a muon, and they have shown that the proton radius is little different [1]. 3, we generalize our analysis by inserting a Coulomb-type central potential by modifying the mass term of the Klein–Gordon equation and determining solutions of bound states for the scalar field subject to the effects of the LSV; in Sect.

Results

Conclusion