Runge–Gross theorem

The Runge -Gross theorem (after Erich Runge and Eberhard KU Gross) is the formal basis of the time-dependent density functional theory, and shows that for a many-particle for every initial state ( wave function at the time ) a unique mapping between the electron density at any point and the outer ( time-dependent ) there is potential (to a additive dependent only on the time term).

The derivation is carried out in two steps:

The positive statement about the existence of this figure makes it possible the dynamics of quantum mechanical Vielteilchenprobleme be calculated using the electron density alone.