Solar energy paper index
Bound state solutions of the Schrödinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods
One-line summary
A solar energy research paper on Bound state solutions of the Schrödinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods.
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Chinese explanation / 中文解读
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Original 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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