Use the method of stationary phase to consider the behavior of the
transmitted packet. In particular, determine the time
at which the center of the reflected pack reaches the point
. From 
and the speed of the center of the packet in
the classically allowed regions, determine
the effective amount of time spent in the forbidden region, 
, and
the effective velocity in that region, 
. What
energy does this velocity correspond to classically? Is there any appreciable
spreading of the reflected packet beyond what you would expect from the
Heisenberg Uncertainty principle?