非相对论电子对的格林函数与LDOS
Green's function and LDOS for non-relativistic electron pair
AI总结：
将非相对论带电粒子的库仑格林函数扩展至双电子排斥相互作用，推导包含自旋与泡利不相容原理的封闭形式积分表达式，计算局部态密度并分析伪LDOS的抑制效应。
摘要：
将处于吸引力库仑力场中非相对论带电粒子的库仑格林函数（GF）扩展，以描述两个非相对论电子通过排斥性库仑力的相互作用。在无电子自旋的情况下，推导出GF的封闭形式表达式，表示为一维积分。随后将结果推广至包含电子自旋并考虑泡利不相容原理。这导致最终的GF由两个分量组成，一个对交换粒子为偶，另一个为奇，其封闭形式表达式表示为一维积分。给出了与自旋无关势的Dyson方程。计算了局部态密度（LDOS），它是偶GF和奇GF贡献的组合。该计算揭示了LDOS对电子间距离和能量的依赖性。单独分析了泡利不相容原理的影响。考察了源于格林函数双体贡献的伪LDOS。该项确保了在~$r=0$处LDOS的完全抑制，并展现出受限的空间范围。阐明了该伪LDOS出现的原因。
英文摘要：
The Coulomb Green's function (GF) for non-relativistic charged particle in field of attractive Coulomb force is extended to describe the interaction of two non-relativistic electrons through repulsive Coulomb forces. Closed-form expressions for the GF, in the absence of electron spins, are derived as one-dimensional integrals. The results are then generalized to include electron spins and account for the Pauli exclusion principle. This leads to a final GF composed of two components, one even and the other odd with respect to exchange particles, with closed-form expressions represented as one-dimensional integrals. The Dyson equations for spin-independent potentials is presented. The local density of states (LDOS) is calculated, which is a combination of contributions from both even and odd GFs. This calculation reveals the dependence of LDOS on inter-electron distance and energy. Separate analysis of the impact of the Pauli exclusion principle is provided. An examination of the pseudo-LDOS, arising from the two-body contribution to the Green's function, is undertaken. Complete suppression of the LDOS at~$r=0$ is ensured by this term, which exhibits a restricted spatial extent. The reasons for the emergence of this pseudo-LDOS are elucidated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
