Bound state solutions of the Schr\"odinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods

Abstract:We investigate the bound state properties of the hydrogen-like atoms in the radial screened Coulomb potential (RSCP). using three complementary analytical approaches - expectation values with Coulomb and Kratzer reference states, variational optimization with a scaled Kratzer basis, and the Hellmann-Feynman theorem - we derive approximate energy eigenvalues as function of the screening parameter c. Benchmarked against high-precision generalized pseudospectral data, the expectation value-approach with the Kratzer basis achieves relative errors of 0.63% for the first ten s-states at $c=0.1$, while the variational method improves this further. The formalism extends naturally to Positronium, demonstrating its generality for arbitrary reduced-mass systems. The complementary biases of the methods provide robust error estimation for plasma-embedded atoms.

J.2; G.1.6; G.1.7; G.4

arXiv:2607.19197 [quant-ph]

(or arXiv:2607.19197v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.19197 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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