Quantum Mechanics: Phase Velocity Vs Group velocity: Wave Dispersion
Above is a good animation to visualise the features of phase velocity of quantum wave and classical wave.
A resultant wave is a linear combination of different waves' wavelength and amplitude. If we change these two parameter, the resultant wave will change correspondingly.
Now we move the wave, we can observe the change in the resultant wave is periodic. The resultant pattern moves at a different speed than the original waves. The speed of each original wave as the phase velocity, while the speed of the resultant pattern as the group velocity.
For quantum particle, the group velocity determines the velocity of the particle. We can describe the motion of the wave by using the wave function, which can be thought of a linear combination in wavelengths. For particle wave function, waves with a shorter wavelength have a faster phase velocity.
For classical water waves on the surface of an ocean, the waves with a shorter wavelength have a slower phase velocity (deep waver).
