Just another conditionally-solvable non-relativistic quantum-mechanical model

TL;DR

This paper presents a conditionally solvable non-relativistic quantum model, providing exact solutions and comparing them with numerical results to deepen understanding of the problem's mathematical structure.

Contribution

It introduces a new conditionally solvable quantum model and derives exact eigenvalues and eigenfunctions, enhancing analytical approaches in quantum mechanics.

Findings

Exact eigenvalues and eigenfunctions obtained

Comparison with numerical eigenvalues confirms accuracy

Discussion of Frobenius method's role in solutions

Abstract

We show that a perturbed Coulomb problem discussed recently is conditionally solvable. We obtain the exact eigenvalues and eigenfunctions and compare the former with eigenvalues calculated by means of a numerical method. We discuss the meaning of the numbers that determine the exact solutions which arise from the Frobenius (power-series) method.