Hello: I need some help with a homework problem that was taken from Quantum Physics by Gasiorowicz. The problem goes like this: You have a beam of electrons and know the size of the wave packet, and by the uncertainty principle you can estimate the dispersion in p at t=0. The problem is to know the size of the wave packet after the beam has crossed 10^4km in two cases: i) when the K.E. of the beam is 13.6 eV and ii) 100MeV. It is clear for me that the wave packet does not have a constant size since the dispersion relation does "disperse"; I also know that in the first case the problem can be treated non-relativistically, while the second case is relativistic. I don't want assume the wave packet to be gaussian. However, I do not know how to combine these ideas to solve the problem.