Suppose that we have a wave packet, in x-space, of a free particle at t=0. How do we find what the wave function will be at time t>0? We know that the time dependent wave packet in its general form is:
So, if we can find the expansion coefficients
, 
, at some time 
,
we can find the wave function at any later time by employing the above
equation. Our first step is then to compute 
.