Differential virial relations in quantum theory and statistical mechanics of some inhomogeneous electron assemblies

摘要

Starting with the canonical or Bloch density matrix for independent electrons moving in a confining potential V(x), a quite general differential virial relation is established in statistical mechanics in one dimension. While such generality is not achieved in two and three dimensions, results are presented for (a) harmonic confinement in both two and three dimensions and (b) a bare Coulomb field in three dimensions. The corresponding fermion ground-state relations in quantum mechanics are finally referred to. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 15]