Kosugi Taichi, Matsushita Yu-Ichiro
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan.
J Phys Condens Matter. 2018 Oct 31;30(43):435604. doi: 10.1088/1361-648X/aae287. Epub 2018 Sep 19.
For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schrödinger 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.
对于一个限制在一维谐振子势阱中、具有有限强度相互作用的三电子系统，我们通过解析求解薛定谔方程得到精确解，并首次明确构建了能量和总自旋的同时本征态。三电子系统的解使我们能够推导出相应两电子系统精确单粒子格林函数（GF）的解析表达式。我们在频域中计算格林函数，以系统地研究其依赖于电子相互作用的行为。我们还比较了使用精确科恩 - 沈（KS）势的非相互作用格林函数与精确格林函数的极点结构，发现对于更强的相互作用，KS系统与原始系统之间的能隙差异更大。我们对实空间中格林函数的行为进行了数值研究，以证明精确格林函数和KS格林函数的形状可能彼此非常不同。我们的简单模型将有助于理解相互作用格林函数的一般特性。
