  Efficient and accurate numerical propagation of the time dependent
Schroedinger equation is a problem with applications across a wide range of
physics. This paper develops an efficient, trivially parallelizeable method for
relaxing a trial wavefunction toward a variationally optimum propagated
wavefunction which minimizes the propagation error relative to a platonic
wavefunction which obeys the time dependent Schroedinger equation exactly. This
method is shown to be well suited for incorporation with multigrid methods,
yielding rapid convergence to a minimum action solution even for Hamiltonians
which are not positive definite.
