AI 中文总结
研究等离子体对类氢原子系统屏蔽效应，用屏蔽库仑势简化方程得BCH本征函数和能量，通过两种解析方法计算能谱，为不同屏蔽范围提供解析公式，建立研究框架并推导热力学性质。
AI 中文摘要
我们使用屏蔽库仑势（即汤川势）对等离子体对类氢原子系统的屏蔽效应进行了非相对论研究。首先将径向薛定谔方程简化为针对基林贝克势的双合流超几何（BCH）方程，该势是屏蔽库仑势的截断形式，并写出精确的BCH本征函数和本征能量。接着研究这些BCH解的局限性，利用BCH函数形式得到适用于弱到中等屏蔽的解析描述。通过两种解析方法计算能谱：直接评估完整汤川哈密顿量期望值和赫尔曼 - 费曼定理，得到积分表示。这些方法为不同屏蔽范围提供了波函数和本征能量的显式解析公式，建立了研究受限量子系统的强大解析框架，还利用BCH公式推导了热力学性质。
英文摘要
We conduct a non-relativistic study of plasma screening effects on hydrogen-like atomic systems using the Screened Coulomb Potential (SCP i.e. Yukawa potential). The radial Schrödinger equation is first reduced to a bi-confluent Heun (BCH) equation for the Killingbeck potential which is the truncated version of the SCP, and we write the exact BCH eigenfunctions and eigenenergies. We then study the limitations of these BCH solutions and obtain an analytic description valid for weak to moderate screening using the BCH functional form. The corrected eigenfunctions are constructed order by order up to O(k^3); they are expressed in terms of the Laguerre polynomials and reduces exactly to Coulomb eigenfunctions when k=0. Using these Functions, the energy spectrum is computed via two analytic methods: (i) direct evaluation of the full Yukawa Hamiltonian expectation value, and (ii) the Hellmann-Feynman theorem, yielding integral representation. All methods presented here provide explicit analytical formulas for both wavefunctions and eigenenergies valid for different ranges of the screening. These methods establish a powerful analytic framework for studying confined quantum systems. The thermodynamic properties are also derived using the BCH formulation.
Comments17 pages, 8 figures and 2 tables
