# Why phase velocity has no physical significance for a matter wave?

The following is quoted from my book:

"The wavelength of a matter wave given by $$λ= \frac{h}{p}$$ has physical significance; its phase velocity $$v_{p}$$ has no physical significance. However, the group velocity of the matter wave is physically meaningful and equals the velocity of the particle."

But why the phase velocity of a matter wave has no physical significance. Can someone please explain? I am so confused. Please help.

The formula, used for a massive particle, and an experiment with a collection of this particle gives the wave behavior which is predicted by quantum mechanics for such ensembles. But the quantum mechanical calculations are not for one particle: The probability of finding a particle in an experiment with the same boundary conditions, is given by $$Ψ^*Ψ$$ where $$Ψ$$ is the quantum mechanical solution of the problem. This wave function is a main postulate of quantum mechanics.
As any phases in this mathematical formulation have to do with the probability, the phases in $$Ψ$$ are not connected to the particle's phase velocity in space. For a free particle the wave function is a plane wave:
$$\Psi(x,t)=Ae^{ikx-i\omega t}$$