Fermion particle density equations in relation to relativistic density functional theory
Faculty of Sciences. Physics
New York, N.Y.
International journal of quantum chemistry. - New York, N.Y.
10th International Conference on the Applications of Density Functional, Theory in Chemistry and Physics, SEP 05-12, 2003, Brussels, BELGIUM
, p. 651-657
Relativistic density functional theory goes back at least to the work of Vallarta and Rosen. This represents the generalization of the Thomas-Fermi method to embody the kinetic energy of an electron of momentum p and rest mass m, as given by special relativity theory in the chemical potential Euler equation. Here we set up a relativistic density functional theory by heuristic arguments that start from well-established exact nonrelativistic differential equations for the Fermion density n(r) in model systems. We focus first on the differential equation of Lawes and March for one-dimensional harmonic confinement. Into their result we introduce the finiteness of the velocity of light c by replacing the Lawes-March differential equation for the Fermion density n(x) by a difference equation for the relativistic Fermion density in which the Compton wavelength h/m(0)c, with m(0) the Fermion rest mass, plays an important role. As we take the nonrelativistic limit c --> infinity, we regain the exact nonrelativistic result. Contact is then established with the Vallarta-Rosen treatment in the limit when a large number N of Fermions are harmonically confined. The remaining models investigated are two-electron in character. Relativistic difference equations to determine the density are again presented, for two such models. (C) 2004 Wiley Periodicals, Inc.