# Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?

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Related: physics.stackexchange.com/q/16063/2451 , physics.stackexchange.com/q/34214/2451 and links therein. –  Qmechanic Sep 12 '12 at 20:05

Actually matter wave describes the probability of finding a particle at any time at any point of space. It is not exactly a sine wave, it is an wave packet. So it contains lots of component of single frequency wave. These the velocity of the single component is called phase velocity. And the overall velocity of composite wave is called the group velocity.

The phase velocity actually don't carry any meaningful physical information for matter wave. All the meaningful information (like, momentum, velocity etc) contains in the group wave. So the velocity of the particle is determined by the group velocity, not phase velocity.

Now since phase velocity does not carry any physical signal, so it can have speed greater than light. It does not violet the theory of relativity. Only the group velocity should be less than speed of light.