  Using a recently developed procedure - multiple wave packet decomposition -
here we study the phase time formulation for tunneling/reflecting particles
colliding with a potential barrier. To partially overcome the analytical
difficulties which frequently arise when the stationary phase method is
employed for deriving phase (tunneling) time expressions, we present a
theoretical exercise involving a symmetrical collision between two identical
wave packets and an one-dimensional rectangular potential barrier. Summing the
amplitudes of the reflected and transmitted waves - using a method we call
multiple peak decomposition - is shown to allow reconstruction of the scattered
wave packets in a way which allows the stationary phase principle to be
recovered.
