On an approximation to the Schr\"odinger equation with the Hellmann potential

TL;DR

This paper critically examines a modified Hellmann potential, revealing that its eigenvalues and spectrum differ significantly from the original, thus questioning its validity and physical relevance.

Contribution

The authors analyze the validity of a recent modification to the Hellmann potential, highlighting discrepancies in eigenvalues and spectrum compared to the original potential.

Findings

Eigenvalues do not match the expected order of the original Hellmann potential.

The spectrum of the modified potential is qualitatively different from the original.

Difficulties in analyzing the main equations were identified.

Abstract

We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the difficulties that we found in the analysis of the main equations and results. We conclude that the eigenvalues reported by the authors do not exhibit the same order as those of the Hellmann potential thus leading to a different underlying physics. What is more: the spectrum of the modified model is qualitatively different from the one supported by the Hellmann potential.