I am trying to understand phase and group velocities in a few different contexts, but require some assistance. From pictures I have seen how these speeds can be different, and I have come to understand that the phase velocity can be greater than the speed of light because it does not actually transport material or energy, that function is reserved for the group velocity of the wave. 1) Now, I am trying to make this a little more concrete in my mind. In the case of an electron, the particle's propagation is governed by the group velocity. So what effect does the phase velocity have on the particle? My book gives an example where an electron's phase velocity (>c) is twice that of its group velocity. What exactly does this velocity represent? Is it possible that this value can be something other than twice the group velocity, and if so, what would actually change? 2) Also, I may be incorrect in saying what follows, so forgive me. Regarding The Uncertainty Principle, a particle can only be found in locations where the group's amplitude is non-zero. So does phase have any relationship to the location of a particle. In some sense, I would think not, because it does not govern the propagation of the particle, but then I don't see what relationship it has to matter waves. 3) Finally, one last clarification of this concept with regards to dispersion. In dielectrics, when the refractive index of light travels through a material at a particular frequency, at times there is a great deal of absorption. This tends to occur at similar frequencies as anomalous dispersion, where the refractive index plummets below one. Again, no laws of physics are violated because only the phase velocity exceeds 'c.' So in this case, what exactly does this phase velocity relate to? Is this purely related to an EM wave, or does this phase velocity describe something related to the material in which radiation is crossing? Thanks in advance!