Show that for your wave function
(Background: Note that
this shows that your results are consistent with the correspondence
principle part of the de Broglie hypothesis, namely that average
behavior of the wave packet evolves according to Newton's Laws. The
result you find here is a specific case of Ehrenfest's theorem which
we will prove in lecture.)
Hint: You should be able to determine ;SPMlt;x;SPMgt; just from the
symmetry of 
. To determine ;SPMlt;p;SPMgt;, consider carefully the two
alternatives of a) using the
momentum operator to compute the average and b) using your previous
results for the Fourier transforms of Gaussians to get 
and then determine the
average value of k from where is centered.