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The N ‐particle wave function as a homogeneous functional of the density
Author(s) -
Gál Tamás
Publication year - 2007
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/qua.21520
Subject(s) - wave function , density functional theory , orbital free density functional theory , homogeneous , generalization , quantum , degree (music) , observable , consistency (knowledge bases) , hybrid functional , function (biology) , physics , quantum mechanics , statistical physics , mathematics , mathematical analysis , geometry , evolutionary biology , acoustics , biology
It is shown that requiring consistency with the structure of the equation that determines the wave function associated to a density ρ() by density‐functional theory, yields the N ‐particle wave function as a degree‐half homogeneous functional of the density, and leads to a separation A [ N , ρ] of N dependence (with N = ∫ρ() d ) of density functionals A [ρ] = A [∫ρ, ρ] for which A [∫ρ, λρ] = λ A [ρ, ρ]; as a consequence of the linearity of quantum mechanical operators. This implies that the ground‐state value of any quantum mechanical observable arises naturally as a degree‐one homogeneous N ‐particle density functional. This general scheme for the structure of density functionals can be considered as the conceptual generalization of the Weizsäcker functional, which is the exact degree‐one homogeneous one‐particle kinetic‐energy density functional. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007