Title
Momentum density and its Fourier transform : relation to the first-order density matrix and some scaling properties Momentum density and its Fourier transform : relation to the first-order density matrix and some scaling properties
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Lancaster, Pa ,
Subject
Physics
Source (journal)
Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015
Volume/pages
64(2001) :4 , p. 1-6
ISSN
1094-1622
1050-2947
1050-2947
Article Reference
042509
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Density-functional theory requires knowledge of the kinetic-energy density t(r) in terms of the ground-state density rho (r). Of course, the direct route to total kinetic energy is from the momentum density n(p), which in turn is directly related by Fourier transform to the first-order density matrix gamma (r,r'). Here, an alternative route to calculate the total kinetic energy is explored, via the Fourier transform (n) over tilde (r) of the momentum density n (p). It is shown that (n) over tilde (r) is related to the density matrix gamma through its contracted form integral gamma (r'-r,r')dr'=(n) over tilde (r). As examples, bare Coulomb field and harmonic confinement for arbitrary numbers of closed shells are treated. Finally, a localized potential V(r) embedded in an initially uniform electron gas is considered, but now to low order in a perturbation series in V(r).
Full text (open access)
https://repository.uantwerpen.be/docman/irua/97d26e/6045.pdf
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