Minimal position-velocity uncertainty wave packets in relativistic and non-relativistic quantum mechanics Original Research Article

We consider wave packets of free particles with a general energy-momentum dispersion relation image. The spreading of the wave packet is determined by the velocity image. The position-velocity uncertainty relation image is saturated by minimal uncertainty wave packets image. In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation image, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation image as well as for the relativistic dispersion relation image. The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.