Open AccessBound states and energy eigenvalues of a radial screened Coulomb potential
Author(s) -
Eric Stachura,
N. Hancock
Publication year - 2021
Publication title -
journal of physics communications
Language(s) - English
Resource type - Journals
ISSN - 2399-6528
DOI - 10.1088/2399-6528/abfff8
Subject(s) - bound state , coulomb , eigenvalues and eigenvectors , ground state , bessel function , physics , hydrogen atom , coulomb wave function , schrödinger equation , upper and lower bounds , quantum mechanics , energy (signal processing) , mathematics , mathematical analysis , electron , group (periodic table)
We analyze bound states and other properties of solutions of a radial Schrödinger equation with a new screened Coulomb potential. In particular, we employ hypervirial relations to obtain eigen-energies for a Hydrogen atom with this potential. Additionally, we appeal to a sharp estimate for a modified Bessel function to estimate the ground state energy of such a system. Finally, when the angular quantum number ℓ ≠ 0, we obtain evidence for a critical screening parameter, above which bound states cease to exist.