  After reexamining the above barrier diffusion problem where we notice that
the wave packet collision implies the existence of {\em multiple} reflected and
transmitted wave packets, we analyze the way of obtaining phase times for
tunneling/reflecting particles in a particular colliding configuration where
the idea of multiple peak decomposition is recovered. To partially overcome the
analytical incongruities which frequently rise up when the stationary phase
method is adopted for computing the (tunneling) phase time expressions, we
present a theoretical exercise involving a symmetrical collision between two
identical wave packets and a unidimensional squared potential barrier where the
scattered wave packets can be recomposed by summing the amplitudes of
simultaneously reflected and transmitted wave components so that the conditions
for applying the stationary phase principle are totally recovered. Lessons
concerning the use of the stationary phase method are drawn.
