Measurement of the velocity of a quantum object: A role of phase and group velocities

•Measurement of velocity of a particle describing by Dirac equation is considered.•Propagation of a wave-packet consisting of relativistic plane waves is studied.•Relations between a measured velocity and the phase and group velocities is established.•The verification of the obtained results has been suggested.

We consider the motion of a quantum particle in a free space. Introducing an explicit measurement procedure for velocity, we demonstrate that the measured velocity is related to the group and phase velocities of the corresponding matter waves. We show that for long distances the measured velocity coincides with the matter wave group velocity. We discuss the possibilities to demonstrate these effects for the optical pulses in coherently driven media or for radiation propagating in waveguides.