  Time-dependent density functionals in principle depend on the initial state
of the system, but this is ignored in functional approximations presently in
use. For one electron it is shown there is no initial-state dependence: for any
density, only one initial state produces a well-behaved potential. For two
non-interacting electrons with the same spin in one-dimension, an initial
potential that makes an alternative initial wavefunction 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.
