There is some discussion in various sources (such as Griffiths Intro to Quantum Mech) about the phase velocity of matter waves (say a beam of monoenergetic nonrelativistic electrons). Some people find that it is smaller than the particle velocity, others that it is superluminal. (The arguments for these two cases are pretty simple and I’d be happy to spell them out if you like.) In contrast, the group velocity equals the particle velocity.
My question is: Do you think there’s any physical significance to the phase velocity of a matter wave? (For example, to be practical, could some experiment--say setting up a standing wave in a Bose-Einstein condensate--reveal its value?)
If in contrast phase velocity is just a mathematical fiction, then I guess there’s little point in arguing about why it has different values depending on how you calculate it.