Center of Mass and Relative Motion in Time Dependent Density Functional Theory
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It is shown that the theorem asserting separability of the center of mass motion for a system of interacting particles in a harmonic external potential is satisfied in the time dependent density functional theory, provided that the exchange-correlation potential satisfies a simple symmetry under transformation to an accelerated frame of reference. Examples of approximations for the exchange-correlation potential which satisfy or violate this symmetry are given.