Group velocity is a property of waves. Without quantum mechanics a particle is not considered a wave so there is no group velocity or phase velocity, only the velocity of the particle.
You can say that the velocity of the particle can't be higher than the speed of light without quantum...
I want to edit my last post but it's too late. :( Here's what I wanted to change:
If we do know its wavelength exactly, we don't know anything about its position so it would not be localized (like a sine wave). On the other hand, if we know its position exactly, we don't know anything about...
The group velocity is the same as the velocity of the particle and can't be higher than the speed of light according to the equations of special relativity.
The phase velocity is the speed of the peaks of the wave and can travel faster than light. The speed of the peaks is more of a...
Thanks everyone for your help. Here's what I've learned:
A wave with a single wavelength is not localized in space. As it turns out (according to Wikipedia), de Broglie didn't propose a single wavelength but a range of wavelengths. When these waves with a range of wavelengths are...
Thanks Dick, your answer helped a lot. Now I understand that the ##v## in ##v = \lambda f## is the phase velocity and the ##v##'s in ##E = \frac{1}{2} m v^2## and ##p = m v## are the group velocity.
I'm still a little confused though. As I understand it, in order to have a group velocity...
The de Broglie equations describing matter waves are $$\lambda = \frac{h}{p} , f = \frac{E}{h} .$$
When these are substituted into ##v = \lambda f## the result is $$v = \frac{E}{p} .$$
Now, when ##E = \frac{1}{2} m v^2## and ##p = m v## are substituted into this equation the result is $$v...