I have some questions about wavepackets.

[dsdsuster]

Hi there
I have some questions about wavepackets. So from my understanding, they are usually a superposition of infinitely many waves of different k (different momentum). However, we can also extract a group velocity that is supposed to correspond to the classical velocity? This group velocity is going to just be a number, with no uncertainty, while the particle's actual velocity has some uncertainty corresponding to the uncertainty in k, the wave number. So what is the group velocity physically if it is not the particle's actual velocity?

I have another separate question about spreading of wavepackets. We typically use some distribution A(k) of wavenumbers that does not change with time to generate the wavefunction. Sometimes the distribution A(k) is obtained from integrating the given wavefunction at time=0. When wavepackets spread, the uncertainty in x increases so shouldn't the distribution A(k) of wavenumbers also change based on the uncertainty principle?

THanks for your help!

 

[azntoon]

The group velocity associated with a wavepacket is an average velocity of the wavepacket over some region of space. It is not necessarily the same as the velocity of a particle that might be associated with the wavepacket, but it can still be used to describe the propagation of the packet in space (and time). As for the spreading of wavepackets, the distribution A(k) of wavenumbers does indeed change as the wavepacket spreads, as the uncertainty principle implies that there must be an uncertainty in both position and momentum for any wavepacket. The exact form of the distribution will depend on the particular wavepacket, but in general the uncertainty in position should lead to an increased uncertainty in momentum, and thus a wider range of wavenumbers.