The group velocity of traveling wave is defined as [tex] v_g =\partial \omega/\partial k[/tex]. I am confused about how to actually calculate this. For instance, in the Schrodinger equation, we find that plane waves solve the equation provided that [tex] \omega = k^2 \hbar/2m[/tex] Does this mean that the group velocity of "Schrodinger waves" is [tex] k\hbar/m[/tex]? Won't this in general depend on the amplitude of the frequency components of a given wave? Given a specific solution to the wave equation how does one answer the question, what is the group velocity of this wave? Edit: related question.... In elementary texts, it is shown how the superposition of two sine waves of equal amplitude and phase but slightly different frequency and speed gives rise to a "traveling envelope", the speed of which we associate with the group velocity. How do we know in general that that superposition of waves gives rise to a well defined envelope?