Comment on: "Rashba coupling induced by Lorentz symmetry breaking effects". Ann. Phys. (Berlin) \textbf{526}, 187 (2013)

TL;DR

This paper critically examines a previous study on Lorentz symmetry breaking effects, clarifying that the original authors only found a single eigenvalue and that their conjecture about cyclotron frequencies was an artifact of their solution method.

Contribution

The paper provides a critical analysis of prior work, highlighting that the earlier results were limited and that the proposed cyclotron frequency conjecture was not physically justified.

Findings

The original spectrum was not fully obtained, only one eigenvalue was found.

The cyclotron frequency conjecture is an artifact of the solution truncation.

The eigenvalue analysis was incomplete and potentially misleading.

Abstract

We analyze the results of a paper on "the arising of a Rashba-like coupling, a Zeeman-like term and a Darwin-like term induced by Lorentz symmetry breaking effects in the non-relativistic quantum dynamics of a spin-1/2 neutral particle interacting with external fields". We show that the authors did not obtain the spectrum of the eigenvalue equation but only one eigenvalue for a specific relationship between model parameters. In particular, the existence of allowed cyclotron frequencies conjectured by the authors is a mere artifact of the truncation condition used to obtain exact solutions to the radial eigenvalue equation.