Here is a link to a course which i am studying, http://quantummechanics.ucsd.edu/ph130a/130_notes/node89.html#derive:timegauss My problem comes from the k' term attached to Vsub(g) (group velocity). I used the substitution k' = k - k(0), factored out all exponentials with no k' dependence, as well grouped the remaining exponentials with a k' dependence with their respective orders. The trouble comes from the term in the second ψ(x,t) integral in the middle of the linked page; i cannot get the k' term on the group velocity*time term in the exponential to disappear. I thought i was being cautious. Any advice?