Momentum density and its Fourier transform: Relation to the first-order density matrix and some scaling properties - art. no. 042509

Density-functional theory requires knowledge of the kinetic-energy density t(r) in terms of the ground-state density rho (r). Of course, the direct ro ute to total kinetic energy is from the momentum density n(p), which in tur n is directly related by Fourier transform to the first-order density matri x gamma (r,r'). Here, an alternative route to calculate the total kinetic e nergy is explored, via the Fourier transform (n) over tilde (r) of the mome ntum density n (p). It is shown that (n) over tilde (r) is related to the d ensity matrix gamma through its contracted form integral gamma (r'-r,r')dr' =(n) over tilde (r). As examples, bare Coulomb field and harmonic confineme nt for arbitrary numbers of closed shells are treated. Finally, a localized potential V(r) embedded in an initially uniform electron gas is considered , but now to low order in a perturbation series in V(r).