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

Authors :
Fernández, Francisco M.
Publication Year :
2023

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.

Subjects

Subjects :
Quantum Physics

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2312.00165
Document Type :
Working Paper