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The stationary phase method is often employed for computing tunneling {\emphase} times of analytically-continuous {\em gaussian} or infinite-bandwidthstep pulses which collide with a potential barrier. The indiscriminateutilization of this method without considering the barrier boundary effectsleads to some misconceptions in the interpretation of the phase times. Afterreexamining the above barrier diffusion problem where we notice the wave packetcollision necessarily leads to the possibility of multiple reflected andtransmitted wave packets, we study the phase times for tunneling/reflectingparticles in a framework where an idea of multiple wave packet decomposition isrecovered. To partially overcome the analytical incongruities which rise upwhen tunneling phase time expressions are obtained, we present a theoreticalexercise involving a symmetrical collision between two identical wave packetsand a one dimensional squared potential barrier where the scattered wavepackets can be recomposed by summing the amplitudes of simultaneously reflectedand transmitted waves.

Recovering the stationary phase condition for accurately obtaining scattering and tunneling times