A most misunderstood conditionally-solvable quantum-mechanical model

TL;DR

This paper clarifies misconceptions about a conditionally-solvable quantum model with Coulomb, linear, and harmonic terms, correcting previous erroneous conclusions through accurate eigenvalue calculations.

Contribution

It provides the correct eigenvalues and eigenfunctions for the model, rectifying prior misunderstandings and demonstrating the importance of proper analysis.

Findings

Previous authors derived incorrect physical conclusions.

The correct eigenvalues are obtained using the Ritz variational method.

The model's true eigenvalues differ significantly from earlier results.

Abstract

In this paper we show that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model. It consists of an eigenvalue equation with seemingly Coulomb, linear and harmonic terms. Here we compare the results derived by those authors with the actual eigenvalues of the models calculated by means of the Ritz variational method.