Bound state solutions of the Schrödinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods

• URL: http://arxiv.org/abs/2607.19197v1
• Date: Tue, 21 Jul 2026 15:31:22 GMT
• Title: Bound state solutions of the Schrödinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods
• Abstract summary: We derive approximate energy eigenvalues as function of the screening parameter c.<n>The formalism extends naturally to Positronium, demonstrating its generality for arbitrary reduced-mass systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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