Bounds for Some Equilibrium Properties of an Electron Gas
Abstract
Upper and lower bounds are derived for the average potential energy and Helmholtz free energy of an electron gas with uniform positive background. In the groundstate limit, upper and lower bounds are given for the average kinetic energy, average potential energy, and total groundstate energy. Inequalities are derived for the static form factor S(k) and wavenumberdependent dielectric function ∊(k, 0), making use of exact sum rules for the Fouriertransformed densitydensity commutator and of the assumption that S(k)<=1. Comparison is made with the exact behavior of these quantities for small k. The sum rules are used to construct an approximate nonlinear integral equation for the groundstate static form factor of the electron gas.
 Publication:

Physical Review A
 Pub Date:
 June 1970
 DOI:
 10.1103/PhysRevA.1.1688
 Bibcode:
 1970PhRvA...1.1688K