Why does the momentum of a matter wave depend on the phase velocity?

[13om13e12]

de Broglie relations say that E = hf and p = h/λ which implies E/p = λf = ω/κ = v_p, or p = E/v_p. It seems to me like the momentum of a particle described by a matter wave should relate to the group velocity not the phase velocity, because the group velocity is generally the actual velocity of the particle.

 

[Bill_K]

They're all related. The phase velocity is E/p while the group velocity is dE/dp. For a particle of mass m, E = p²/2m. So for this case the phase velocity is p/2m and the group velocity is p/m. Looks like the group velocity is what you want to be the "actual" velocity v.