I have some questions about wavepackets.
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!