用三体问题的解析解计算两电子相互作用的单粒子格林函数：与精确Kohn-Sham系统的比较
One-particle Green's function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn--Sham system
摘要：
对于一维谐振子势阱中具有有限强相互作用的三电子系统，通过解析求解薛定谔方程，得到了系统的精确解，并首次明确地构造了系统的能量和自旋的同时本征态.三电子系统的解决方案，使我们能够获得相应的双电子系统的精确的单粒子格林函数（GF）的解析表达式。我们在频域中计算了GF，系统地研究了它的行为取决于电子相互作用。我们还比较了用精确Kohn-Sham（KS）势计算的无相互作用GF的极点结构和用精确GF计算的极点结构，发现相互作用越强，KS系统与原系统的能隙相差越大.我们在实空间中对GF的行为进行了数值研究，以证明精确GF和KS GF可以具有彼此完全不同的形状。我们的简单模型将有助于理解相互作用的GF的一般特征。
英文摘要：
For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schroedinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous eigenstates of the energy and total spin for the first time. The solutions for the three-electron system allow us to derive analytic expressions for the exact one-particle Green's function (GF) for the corresponding two-electron system. We calculate the GF in frequency domain to examine systematically its behavior depending on the electronic interactions. We also compare the pole structure of non-interacting GF using the exact Kohn--Sham (KS) potential with that of the exact GF to find that the discrepancy of the energy gap between the KS system and the original system is larger for a stronger interaction. We perform numerical examination on the behavior of GFs in real space to demonstrate that the exact and KS GFs can have shapes quite different from each other. Our simple model will help to understand generic characteristics of interacting GFs.
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