Comment on: "Harmonic oscillator in an environment with a pointlike defect". Phys. Scr. \textbf{94} ( 2019) 125301

TL;DR

This paper critiques recent findings on a harmonic oscillator with a pointlike defect, clarifying that the previous results were based on misinterpretations and incorrect model assumptions.

Contribution

It clarifies the correct interpretation of the eigenvalue problem and corrects misconceptions in the prior analysis of the harmonic oscillator with a defect.

Findings

Previous oscillator frequencies were misinterpreted

Exact eigenvalues from prior work are model-specific and invalid for the intended system

Correct analysis shows different eigenvalue structure

Abstract

We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally solvable eigenvalue equation. Also the exact eigenvalues derived by those authors are meaningless because they belong to different quantum-mechanical models.