Many-fermion systems: differential equations and kinetic energy functionals for different confining potentials

摘要

Determination of the kinetic energy functional is one of the central problems in the density functional theory of a many-fermion system. We consider several many-fermion systems to be characterized by simple confining potentials: the harmonic oscillator potential in one and three dimensions, the Coulmb potential, and the potential V(x) = -U_osech~2(x/L). We discuss for each of these cases the differential equation that determines the fermion density in the given potential, and the corresponding kinetic energy density.