Fermion particle density equations in relation to relativistic density functional theoryFermion particle density equations in relation to relativistic density functional theory
Faculty of Sciences. Physics
Department of Physics
2005New York, N.Y., 2005
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
101(2005):6, 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.