Unconventional approach to orbital-free density functional theory derived from a model of extended electrons

摘要

An equation proposed by Levy, Perdew and Sahni in 1984 [PRA 30, 2745 (1984)]is an orbital--free formulation of density functional theory. However, thisequation describes a bosonic system. Here, we analyze on a very fundamentallevel, how this equation could be extended to yield a formulation for a generalfermionic distribution of charge and spin. This analysis starts at the level ofsingle electrons and with the question, how spin actually comes into a chargedistribution in a non-relativistic model. To this end we present a space-timemodel of extended electrons, which is formulated in terms of geometric algebra.Wave properties of the electron are referred to mass density oscillations. Weprovide a comprehensive and non-statistical interpretation of wavefunctions,referring them to mass density components and internal field components. It isshown that these wavefunctions comply with the Schr\"odinger equation, for thefree electron as well as for the electron in electrostatic and vectorpotentials. Spin-properties of the electron are referred to intrinsic fieldcomponents and it is established that a measurement of spin in an externalfield yields exactly two possible results. The model agrees with the results ofstandard theory concerning the hydrogen atom. Finally, we analyze many-electronsystems and derive a set of coupled equations suitable to characterize thesystem without any reference to single electron states. The model is expectedto have the greatest impact in condensed matter theory, where it allows todescribe an $N$-electron system by a many-electron wavefunction $\Psi$ of four,instead of 3N variables. The many-body aspect of a system is in this caseencoded in a bivector potential.