  We show that certain types of quantum walks can be modeled as waves that
propagate in a medium with phase and group velocities that are explicitly
calculable. Since the group and phase velocities indicate how fast wave packets
can propagate causally, we propose the use of these wave velocities in a new
definition for the hitting time of quantum walks. The new definition of hitting
time has the advantage that it requires neither the specification of a walker's
initial condition nor of an arrival probability threshold. We give full details
for the case of quantum walks on the Cayley graphs of Abelian groups. This
includes the special cases of quantum walks on the line and on hypercubes.
