Kinetic energy functional derivative for the Thomas-Fermi atom inD 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 Ž . 2rD 1y2rD ground-state density n r proportional to n . But the Poisson equation relates n to ''reduced'' density derivatives n y1Ž d 2 n r d r 2 .. Thus ␦ Tr␦ n 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 s 2.

Flat Thomas-Fermi artificial atoms

“…This makes the differential equation elementary to solve, but of course corresponds not to a "pancake" of point electrons, but to a pool of infinitely long parallel line charges each generating a logarithmic, rather than a point-Coulomb, potential. Thus, it is either a misrepresentation of the actual QD problem [17][18][19][20] or simply an interesting but abstract exercise [21][22][23][24][25].…”