Article
Version 1
Preserved in Portico This version is not peer-reviewed
On the Spectrum of the Screened Coulomb Potential V(r) =
Version 1
: Received: 15 September 2023 / Approved: 19 September 2023 / Online: 20 September 2023 (05:00:30 CEST)
How to cite: Fernandez, F. On the Spectrum of the Screened Coulomb Potential V(r) =. Preprints 2023, 2023091322. https://doi.org/10.20944/preprints202309.1322.v1 Fernandez, F. On the Spectrum of the Screened Coulomb Potential V(r) =. Preprints 2023, 2023091322. https://doi.org/10.20944/preprints202309.1322.v1
Abstract
We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$. The well known Hellmann-Feynman theorem shows that all the bound states of the Coulomb potential ($C=0$) remain bounded as $C$ increases. We derive a simple approximate analytical expression for the eigenvalues for sufficiently small values of the screening parameter $C$ and an approximate asymptotic expression for the asymptotic behaviour of the s-state eigenvalues when $C\rightarrow \infty $. Present results are expected to resolve the discrepancy about the spectrum of the quantum-mechanical model just mentioned.
Keywords
screened Coulomb potential; radial Schrödinger equation; Hellmann-Feynman theorem; critical values
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
