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The basic formalism of density functional theory (DFT) has a simple and appealing structure which gives an interesting perspective on the quantum mechanics of many-body systems. This structure centers on the properties of a functional of the density F[&rho], that gives the minimum of the kinetic-plus-Coulomb-interaction energy compatible with the density &rho (of a system of a fixed number N of electrons), and which is the modern descendant of the "universal functional" of Hohenberg and Kohn. Unfortunately, F[&rho] is ill-behaved in some ways and it is not clear that it has the properties the formalism requires (more-or-less strongly). There are at least three ways to deal with this situation: ignore it (the preferred solution to date), bite the bullet and litter the formalism with complicated conditions and emendations (assuming appropriate ones can be found), or re-interpret the formalism. I have investigated the last possibility, taking "density" in a coarse-grained sense. The coarse grained models turn out to be (are proven to be) very nicely behaved, as reported in a pair of papers, here (published in Journal of Chemical Physics) and here (an early version of which appeared in Physical Review A).

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P. E. Lammert : foundations of density functional theory