2003/05/17 by Taichi Kosugi, Yu‐ichiro Matsushita, Yu-ichiro Matsushita +2
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Density functional theory #Eigenvalues and eigenvectors #Electron #Exact solutions in general relativity #Function (biology) #Kohn–Sham equations #Organic and Molecular Conductors Research #Particle system #Physics #Quantum and electron transport phenomena #Quantum mechanics #Schrödinger equation #cond-mat.mes-hall
paper · pdf · doi:10.1088/1361-648x/aae287
published as J. Phys.: Condens. Matter 30 (2018), 435604 · to be published in Journal of Physics: Condensed Matter
openalex publication_date 2003/05/17 · openalex created_date 2016/06/24 · arxiv created 2018/09/20 · arxiv updated 2018/11/14 · openalex updated_date 2026/06/11
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.