(5.4.3) Chattaraj : The density (its advantage over the wave function), density matrices (writing energy in terms of them), and density functionals (a map from a function to a number) should be introduced. DFT highlights the fact that, as N and v(r) fix the Hamiltonian, the Schrödinger equation is a map from these quantities to the density, whereas the corresponding inverse map (along with normalization) is DFT. Of course, Kato's cusp condition for the ground state of any system, provides v(r) through nuclear positions and the charges, in case the density is known. Various techniques (Kohn-Sham, Levy-Lieb, orbital-free DFT, etc.) exist for calculating the density. A recapitulation of Hartree-Fock theory may be helpful.