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Kinetic energy functional derivative for the Thomas–Fermi atom in D dimensions
Author(s) -
March Norman H.,
Kais Sabre
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)65:5<411::aid-qua5>3.0.co;2-z
Subject(s) - thomas–fermi model , atom (system on chip) , derivative (finance) , kinetic energy , mathematical physics , functional derivative , fermi gamma ray space telescope , ground state , poisson's equation , poisson distribution , quantum mechanics , density functional theory , physics , chemistry , mathematics , computer science , financial economics , economics , embedded system , electron , statistics
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 derivatives n −1( d 2 n / dr 2 ) . Thus δ T /δ 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 =2. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 411–413, 1997