Effects of a background scalar field induced by the Lorentz symmetry violation on Non Relativistic Quantum Mechanics

TL;DR

This paper explores how a background scalar field, arising from Lorentz symmetry violation, modifies the Schrödinger equation and affects quantum systems like particles in a potential well and harmonic oscillator.

Contribution

It introduces a novel extension of the Schrödinger equation incorporating a background scalar field inspired by Lorentz symmetry violation models.

Findings

Modified energy spectra for particle in a well and harmonic oscillator

Altered wavefunction behaviors due to the scalar field

Potential implications for quantum systems under Lorentz violation

Abstract

The extension of Standard Model of the Fundamental Particles which consider the Lorentz Symmetry Violation governed by a background tensor field presented by Colladay and Kostelecky consider the hypothesis of having a privileged direction in the space-time. Here we investigated a extension of the Schr\"odinger Equation inspired on that model taking into account a background scalar field. We analyze the behavior of this modified Schr\"odinger equation on a particle trapped in a well and quantum harmonic oscillator.