Question

The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
$E=hv,p=\frac{h}{\lambda }$
But while the value of $\lambda$ is physically significant, the value of $v$ (and therefore, the value of the phase speed $v$ $\lambda$) has no physical significations. Why?

Answer 1

The absolute value of energy E (but not momentum p) of any particle is arbitrary to within an additive constant. Hence, while is physically significant, the absolute value of a matter-wave of an electron has no direct physical meaning. The phase speed is likewise not physically significant. The group speed given by $\frac{dv}{d\left(1/\lambda \right)}=\frac{dE}{dp}\left(\frac{p^2}{2m}\right)=\frac{p}{m}$, is physically meaningful.