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

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.