  Historically the starting point of wave mechanics is the Planck and
Einstein-de Broglie relations for the energy and momentum of a particle, where
the momentum is connected to the group velocity of the wave packet. We
translate the arguments given by de Broglie to the case of a wave defined on
the grid points of a space-time lattice and explore the physical consequences
such as integral period, wave length, discrete energy, momentum and rest mass.
