On the misinterpretation of conditionally-solvable quantum-mechanical problems

TL;DR

This paper critically examines the solutions of certain quantum-mechanical models, revealing that recent exact solutions are incorrect due to violations of fundamental theorems, and clarifies the origin of these errors.

Contribution

It demonstrates that previous solutions to some quantum models are invalid and provides insight into the source of these inaccuracies using the Frobenius method.

Findings

Recent solutions do not satisfy well-known theorems

Incorrect solutions are identified in radial eigenvalue equations

Clarification of the origin of the solution errors

Abstract

We apply the Frobenius (power-series) method to some simple exactly-solvable and conditionally-solvable quantum-mechanical models with supposed physical interest. We show that the supposedly exact solutions to radial eigenvalue equations derived in recent papers are not correct because they do not satisfy some well-known theorems. We also discuss the origin of the mistake by means of the approach indicated above.