Harmonic oscillator dynamics with an attractive inverse-square interaction induced by Lorentz symmetry breaking

This is the authors' abstract. We don't add key points for this paper.

This work explores an extension beyond the Standard Model, examining the quantum effects of an attractive inverse-square interaction within a harmonic oscillator potential. Such studies are relevant to areas including the Efimov effect, black hole physics, and atomic interactions. Recent research has investigated attractive inverse-square potentials in the presence of a fixed background vector that breaks Lorentz symmetry. Building on this approach, we analyze the effects of Lorentz symmetry violation for a neutral particle interacting with an attractive inverse-square nonuniform electric field in the presence of a harmonic oscillator potential. In the low-energy limit, we derive the bound state solutions for the particle in this specific scenario.