Density functional theory/Hohenberg–Kohn theorems
1. If two systems of electrons, one trapped in a potential and the other in , have the same ground-state density then necessarily .
Corollary: the ground state density uniquely determines the potential and thus all properties of the system, including the many-body wave function. In particular, the "HK" functional, defined as is a universal functional of the density (not depending explicitly on the external potential).
2. For any positive integer and potential it exists a density functional such that obtains its minimal value at the ground-state density of electrons in the potential . The minimal value of is then the ground state energy of this system.