Abstract

KELLER, Jaime. The Foundations of Density Functional Theory and Wave Quantum Mechanics. Rev. Soc. Quím. Méx [online]. 2000, vol.44, n.1, pp.22-28. ISSN 0583-7693.

We analyze the notion of Density Functional Theory from the definition of a density of action over spacetime. We derive a theory to obtain the energy as a function of particle density, which contains the standard Density Functional Theory (DFT) and enlarges it by considering in one functional both the density of particles and the energy density per particle. The formulation presents a mathematical structure where the particle density is a factor of the energy per particle. The starting point is the definition of a global action density K(x) from which, by successive projections, the density K_j for a given type j of particles is projected. This density is then factorized into gauge dependent factors, which are shown to generate known relations and structures of quantum mechanics. Within DFT the minimization of the energy density functional, with respect to changes in the density, contains as a consequence two terms: the first corresponds to the standard density functional theory for non-interacting particles, and the second to the optimization of the kinetic and the interparticle interaction energy, terms that go beyond the standard DFT. We show explicitly the relation of the present approach to standard Wave Quantum Mechanics and show explicitly the reasons within space-time-action of several basic postulates of Quantum Mechanics.

Keywords : Density functional theory; fundations of quantum mechanics; principle of choice (PC).

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