First-degree homogeneous N-particle noninteracting kinetic-energy density functionals - art. no. 062503

It is known in density-functional theory that the noninteracting kinetic-en ergy density functional T-s[rho] is not first-degree homogeneous in density scaling. However, it is shown here that, for every particle number N, ther e is an N-particle noninteracting kinetic-energy density functional T-N[rho ], that is, a density functional that gives the noninteracting kinetic ener gy for N-particle densities, which is of first-degree homogeneity in the de nsity rho((r) over bar). This gives a powerful tool, a strong requirement, for constructing such functionals. A systematic procedure to obtain the rea l part of T-N[rho], the full T-N[rho] in one-dimension, for each N is also proposed, It is pointed out, further, that in the Euler-Lagrange equations that determine the one-particle orbitals that define T-s[rho], the Lagrange multiplier that forces the orbitals to yield rho((r) over bar) is not othe r than the first derivative of T-s[rho], deltaT(s)[rho]/delta rho((r) over bar), which yields a natural derivation of the Kohn-Sham equations. Utilizi ng the same idea, it is shown for ground states how the Schrodinger equatio n can be derived from the basics of density-functional theory as well.