Bounds for Some Equilibrium Properties of an Electron Gas

1970/06/01 by Alfred A. Kugler · 5 citations
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Advanced Thermodynamics and Statistical Mechanics #Electrostatics and Colloid Interactions

paper · doi:10.1103/physreva.1.1688

openalex publication_date 1970/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ground-state limit, upper and lower bounds are given for the average kinetic energy, average potential energy, and total ground-state energy. Inequalities are derived for the static form factor S(k) and wave-number-dependent dielectric function \ensuremathε(k, 0), making use of exact sum rules for the Fourier-transformed density-density commutator and of the assumption that S(k)\ensuremath≤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 ground-state static form factor of the electron gas.

Citations

• New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem

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