与径向屏蔽库仑势相互作用的原子系统薛定谔方程的束缚态解：解析近似方法
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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中文总结 AI 辅助
研究处于径向屏蔽库仑势中类氢原子束缚态性质，采用三种解析方法推导近似能量本征值，与高精度数据对比，前十个s态在c = 0.1时相对误差0.63%，变分方法可改进，还扩展到正电子素，为等离子体中原子提供误差估计。
中文摘要 AI 辅助
我们研究了处于径向屏蔽库仑势（RSCP）中的类氢原子的束缚态性质。使用三种互补的解析方法——基于库仑和克拉策尔参考态的期望值、用缩放后的克拉策尔基进行变分优化以及赫尔曼 - 费曼定理——我们推导了作为屏蔽参数c的函数的近似能量本征值。与高精度广义伪谱数据对比，使用克拉策尔基的期望值方法在c = 0.1时前十个s态的相对误差为0.63%，变分方法进一步改进了这一结果。该形式体系自然地扩展到了正电子素，证明了其对任意约化质量系统的通用性。这些方法的互补偏差为等离子体中嵌入的原子提供了可靠的误差估计。
英文摘要
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.
