1
$\begingroup$

I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I couldn't find any answers that address mine.

So, I understand that group velocity is the velocity of the wave 'envelope' (i.e. outline shape) of a collection of superimposed travelling waves. However, is it the case that, for any arbitrary collection of such travelling waves, there will always be a wave envelope that retains the same shape as the collection of waves propagate? Or, will that happen only in certain situations, or for certain combinations of waves? Will any arbitrary collection of waves have a group velocity?

$\endgroup$
2
$\begingroup$

For any arbitrary collection of such travelling waves will always be a wave envelope that retains the same shape as the collection of waves propagate?
No, it will not. For example, a Gaussian wave-packet will spread out in time. Wave packets are used to represent localization of particles in Quantum Mechanics.Group velocity will give the physical velocity of the particle. For example, a moving electron can be represented by a wave-packet whose group velocity will give the velocity of the particle.

$\endgroup$
  • $\begingroup$ Thanks for your answer Goobs. So, if I understand this correctly, if the phase velocities of the different frequency components are all equal, then the envelope shape will be maintained and group velocity equals phase velocity. However, if the phase velocities are different, then the envelope will stretch/distort (dispersion)? $\endgroup$ – Time4Tea Apr 29 '15 at 0:11
  • $\begingroup$ So, is group velocity sort of like an average of the phase velocities? $\endgroup$ – Time4Tea Apr 29 '15 at 0:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.