Demonstration of initial-state dependence in time-dependent density-functional theory

Time-dependent density functionals depend in principle on the initial state of a system, but this is ignored in functional approximations presently in use. For one electron, it is shown that there is no initial-state dependence: for any density, only one initial state produces a well-behaved potential. For two noninteracting electrons with the same spin in one dimension, an initial potential that makes an alternative initial wave function evolve with the same density and current as a ground state is calculated. This potential is well-behaved, and can be made arbitrarily different from the original potential.