The following wave packet describes a familiar event involving a classical particle:
where
Note: 
.
Figure 4: Position of Wave Packet
a) Using the method of stationary phase, determine
, the location of the first part of the wave packet
at time t. Sketch the path followed by the
first packet 
on Figure 4.
Give the trajectory both for times t;SPMgt;0 and
times t;SPMlt;0.
Hint: After deriving your final result, use
the definition 
to simplify your result.
b) Using the method of stationary phase, determine 
,
the location of the second part of wave packet at time t.
Sketch the path followed by the second packet 
on
Figure 4. Give the trajectory
both for times t;SPMgt;0 and times t;SPMlt;0.
Hint: After deriving your final result, use the definition to simplify your result.
c) Keeping in mind that by definition, 
for x;SPMgt;0 for all
t, so that the wave packet may never be centered around positions
x;SPMgt;0, describe in a short sentence the classical behavior
of a particle described by the total wave packet
.