In many

Hohenburg-Kohn Theorems It can be seen that the density functionals significantly reduce the computaional complexity in many ways, but the question is, did the single electron density tell you all needed for calculating the ground state energy of a many-body quantum system. A short answer is yes. The following Hohenburg-Kohn theorems state the relation between ground state energy and the electron density. Theorem 1. The ground-state energy and all other ground-state electronic properties are uniquely determined by the electron density.

The Bra-ket notation In quantum mechanics, bra–ket notation, or Dirac notation, is used ubiquitously to denote quantum states. The notation uses angle brackets, $\displaystyle \langle$ and $\displaystyle \rangle$, and a vertical bar $\displaystyle |$, to construct “bras” and “kets”.