Physical properties of de Broglie's phase waves

An account of de Broglie's introduction of phase waves is given that emphasizes that they are a relativistic concept. The properties of the frequency, wavelength, and velocity of de Broglie waves are found under a Lorentz transformation. A nonrelativistic specialization of phase waves is obtained, and the appropriate frequency, wavelength, and velocity are defined. The transformation properties of these parameters under a Galilean transformation are given. The concept of a group velocity for phase waves is re-examined and shown to be applicable.