Demonstration of initial-state dependence in time-dependent density-functional theory - art. no. 042501

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 dependen ce: for any density, only one initial state produces a well-behaved potenti al. For two noninteracting electrons with the same spin in one dimension, a n initial potential that makes an alternative initial wave function evolve with the same density and current as a ground state is calculated. This pot ential is well-behaved, and can be made arbitrarily different from the orig inal potential.