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

✍ Scribed by Norman H. March; Sabre Kais

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 116 KB
• Volume: 65
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)65:5<411::aid-qua5>3.0.co;2-z

✦ Synopsis

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.