Runge-Gross Theorem
Michael Rose
The Runge-Gross Theorem is a proof showing that for an electron density evolving in time according to a time-dependent scalar potential, there is a one-to-one mapping between the electron density and that scalar potential. Thus, if we have two systems, with the same initial electron density but evolving according to two distinct time-dependent external potentials, after even an infinitesimally small amount of time has transpired, the resulting densities will no longer be equivalent.
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