Comment on: "On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the harmonic oscillator''. Eur. Phys. J. Plus (2012) \textbf{127}: 102

TL;DR

This paper critiques a previous study on bound states of a neutral particle influenced by Lorentz symmetry breaking, revealing that the original truncation method only finds one energy level and overlooks others, with the cyclotron frequency dependence being an artifact.

Contribution

It clarifies the limitations of the truncation condition used in prior work, showing it only yields a single bound state and is not essential for bound state existence.

Findings

The original truncation condition finds only one energy eigenvalue.

The cyclotron frequency dependence is an artifact of the truncation.

Other bound states are missed by the original method.

Abstract

We analyze the calculation of bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by Lorentz symmetry breaking effects. We show that the truncation condition proposed by the authors only provides one energy eigenvalue for a particular model potential and misses all the other bound-state energies. The dependence of the cyclotron frequency on the quantum numbers is a mere artifact of the truncation condition that is by no means necessary for the existence of bound states.