KINETIC-ENERGY FUNCTIONAL DERIVATIVE FOR THE THOMAS-FERMI ATOM IN D-DIMENSIONS

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 n(2/D). But the Poisson equation relates n(1-2/D) to ''reduced'' density derivativ es n(-1(d2n/dr2)). Thus delta T/delta n can be written also, quite com pactly, solely in terms of these derivatives. An analytic solution to the Thomas-Fermi equation in D dimensions can be presented as an expan sion about the known analytic solution at D = 2. (C) 1997 John Wiley & Sons, Inc.