2009/12/22 by Pierre-François Loos, Peter M. W. Gill · 38 citations
Physics and Astronomy · #Electron #Energy (signal processing) #Helium #Kinetic energy #Limit (mathematics) #Limiting #Quadratic equation #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics #cond-mat.other
paper · pdf · doi:10.1063/1.3275519
published in The Journal of Chemical Physics 131(24), 241101 (American Institute of Physics) · 4 pages, 0 figure
openalex publication_date 2009/12/22 · arxiv created 2010/02/17 · arxiv updated 2010/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the high-density-limit correlation energy E(c) in D > or = 2 dimensions for the (1)S ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the E(c) values are strikingly similar, depending strongly on D but only weakly on the external potential. We conjecture that for large D, the limiting correlation energy E(c) approximately -delta(2)/8 in any confining external potential, where delta = 1/(D-1).