  We analytically compute the time evolution of an initial infinite plane wave
in the presence of a 1-dimensional square quantum barrier. This calculation
generalizes the analysis of the shutter problem and sets the basis for the
calculation of the transmission of general wave packets, aiming to work out the
explicit contribution of the resonant (Gamow) states. The method relies mainly
on the analytical properties of the Green function. The role of separate
boundary conditions on the Green function and on the evolution equation is
highlighted. As in previous works on related problems, only the determination
of the resonant momenta requires numerical methods.
