Kinetic energy functional derivative for the Thomas–Fermi atom in D dimensions

Abstract

The self-consistent Thomas–Fermi atom satisfying Poisson's equation in D dimensions has a functional derivative of the kinetic energy T with respect to the ground-state density n(r) proportional to n2/D. But the Poisson equation relates n1−2/D to “reduced” density derivatives n. Thus δT/δn can be written also, quite compactly, solely in terms of these derivatives. An analytic solution to the Thomas–Fermi equation in D dimensions can be presented as an expansion about the known analytic solution at D=2. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 411–413, 1997