  This report deals with the basic concepts on deducing transit times for
quantum scattering: the stationary phase method and its relation with delay
times for relativistic and non-relativistic tunneling particles. We notice that
the applicability of this method is constrained by several subtleties in
deriving the phase time that describes the localization of scattered wave
packets. We investigate the general relation between phase times and dwell
times for quantum tunneling/scattering. Considering a symmetrical collision of
two identical wave packets with an one-dimensional barrier, we demonstrate that
these two distinct transit time definitions are explicitly connected. The
traversal times are obtained for a symmetrized (two identical bosons) and an
antisymmetrized (two identical fermions) quantum colliding configuration.
Multiple wave packet decomposition shows us that the phase time (group delay)
describes the exact position of the scattered particles and, in addition to the
exact relation with the dwell time, leads to correct conceptual understanding
of both transit time definitions. At last, we extend the non-relativistic
formalism to the solutions for the tunneling zone of a one-dimensional
electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave
equation where the incoming wave packet exhibits the possibility of being
almost totally transmitted through the potential barrier. The conditions for
the occurrence of accelerated tunneling transmission probabilities are all
quantified and the problematic superluminal interpretation based on the
non-relativistic tunneling dynamics is revisited.
