#### Title

Energy in a finite two-dimensional spinless electron gas

#### Document Type

Article

#### Publication Date

5-1-2013

#### Abstract

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. © 2013 © 2013 Author(s).

#### Recommended Citation

Ciftja, O., Sutton, B., & Way, A. (2013). Energy in a finite two-dimensional spinless electron gas. Retrieved from https://digitalcommons.pvamu.edu/chemistry-physics-facpubs/206