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

Francisco M. Fernández

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arXiv · 2312.00165

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

Francisco M. Fernández

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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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Francisco M. Fernández. 2023-09-15. On the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$. https://arxiv.org/abs/2312.00165

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