Show that, for this potential, the time delays 
and
for emergence of the center of the transmitted packet from the
point x=a and for the emergence of the center of the reflected
packet from the point x=0 are always equal.
Hint: To show this it is not necessary to
compute the phase derivatives of the quantum amplitudes. You should
be able to show that the phases of your quantum amplitudes
always differ by a constant, and reason from there.
Next, evaluate the time delay 
in the two special
cases 
and 
for 
.
Hint: Use the fact that the phase of 1/(a+bi) is 
, and take the derivative in the logarithmic
form noting immediately which 
or 
terms are zero or one.
Also, don't forget dk'/dk=k/k'.
When k';SPMlt;;SPMlt;k, one of the time-delay cases or corresponds to the solver movie showing a wave packet trapped on
top of a potential barrier such as the one in this problem. Which
case is it? Why?