Density functional theory and the von Weizsacker method

Abstract

The response function of a uniform extended system of noninteracting fermions, and thus the energy of a weakly perturbed system of this kind, is computed exactly and in the von Weizsacker approximation; it is thus shown that (a) the original von Weizsacker coefficient leads to an upper bound to the energy which becomes asymptotically exact for short wavelength perturbations and (b) the coefficient reduced by a factor of 9 leads to a lower bound which becomes asymptotically exact for long waves. Generalisations of these results are discussed for the case when the fermions are interacting electrons.