Show that the time delay between when the center of an incoming
packet centered around energy 
hits the barrier at x=0 and
the the time when center of the reflected packet leaves the point
x=0 is given by
where 
is the classical velocity of the particle in the
barrier region (0 ;SPMlt; x ;SPMlt; L), 
and 
are the de Broglie wave
vectors in the regions x ;SPMlt; 0 and 0 ;SPMlt; x ;SPMlt; L respectively, and
.
For the first case you sketched in 4.3 ( 
,
), how does the time spent by the packet in the
barrier region 0 ;SPMlt; x ;SPMlt; L compare to the time expected classically?
Qualitatively, how does the appearance of your wave function 
reflect the amount time spent by the particles in the barrier region?
For the second case you sketched in 4.3 ( ,
), how does the time spent by the packet in the
barrier region 0 ;SPMlt; x ;SPMlt; L compare to the time expected classically?
Qualitatively, how does the appearance of your wave function
reflect the amount time spent by the particles in the barrier region?
These states are referred to as resonances.