Open AccessEnergy in a finite two-dimensional spinless electron gas
Author(s) -
Orion Ciftja,
Bradley P. Sutton,
Ashley Way
Publication year - 2013
Publication title -
aip advances
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 58
ISSN - 2158-3226
DOI - 10.1063/1.4804933
Subject(s) - electron , physics , coulomb , fermi gas , quantum mechanics , spin (aerodynamics) , square (algebra) , limit (mathematics) , energy (signal processing) , thermodynamic limit , hartree–fock method , coulomb's constant , quantum electrodynamics , condensed matter physics , coulomb barrier , mathematical analysis , mathematics , geometry , thermodynamics
We study the properties of a finite two-dimensional electron gas system in the Hartree-Fock approximation. We obtain exact analytical expressions for the energy in a finite two-dimensional fully spin-polarized (spinless) system of electrons interacting with a Coulomb potential immersed in a finite square region uniformly filled with a neutralizing positive charge. The difficult two-electron integrals over the finite square domain are reduced to simple compact expressions involving analytic auxiliary functions. We provide results for the potential energy of systems with a finite number of electrons and show how the energy slowly converges towards its thermodynamic limit bulk value