Comment on: "Bound states and the potential parameter spectrum". J. Math. Phys. \textbf{67}, 062103 (2020)

TL;DR

This paper critiques the application of the tridiagonal representation approach to certain quantum models, highlighting a flaw in its analysis of the Kratzer-Fues potential and advocating for the simpler Frobenius method.

Contribution

It identifies a flaw in the TRA method for specific quantum models and demonstrates that the Frobenius method provides a more accurate and elegant solution.

Findings

TRA contains a serious flaw for Kratzer-Fues potential

Frobenius method yields correct, simpler solutions

TRA's results are invalidated by the identified flaw

Abstract

We analyze the application of the "tridiagonal representation approach" (TRA) to the Schr\"{o}dinger equation for some simple, exactly-solvable, quantum-mechanical models. In the case of the Kratzer-Fues potential the mathematical reasoning appears to exhibit a serious flaw that invalidates the result and the expression for the energy does not appear to be correct. We also show that the well known Frobenius method, which resembles the TRA, is far simpler, clearer and more elegant; in addition to give the correct result.