  The stationary phase method is often employed for computing tunneling {\em
phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth
step pulses which collide with a potential barrier. The indiscriminate
utilization of this method without considering the barrier boundary effects
leads to some misconceptions in the interpretation of the phase times. After
reexamining the above barrier diffusion problem where we notice the wave packet
collision necessarily leads to the possibility of multiple reflected and
transmitted wave packets, we study the phase times for tunneling/reflecting
particles in a framework where an idea of multiple wave packet decomposition is
recovered. To partially overcome the analytical incongruities which rise up
when tunneling phase time expressions are obtained, we present a theoretical
exercise involving a symmetrical collision between two identical wave packets
and a one dimensional squared potential barrier where the scattered wave
packets can be recomposed by summing the amplitudes of simultaneously reflected
and transmitted waves.
