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-3(d2n/dr2). 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.
|Number of pages||3|
|Journal||International Journal of Quantum Chemistry|
|Publication status||Published - 1 Jan 1997|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry