Related papers: On the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$

On the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$

URL: http://arxiv.org/abs/2312.00165v1
Date: Fri, 15 Sep 2023 18:34:08 GMT
Title: On the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$
Authors: Francisco M. Fern\'andez
Abstract summary: We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r-1e-C/r$. We derive a simple approximate analytical expression for the eigenvalues for sufficiently small values of the screening parameter $C$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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