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The principle of relativity and the de Broglie relation
Authors: Julio Güémez, Manuel Fiolhais, Luis A. Fernández
Ref.: American Journal of Physics 84, 443-447 (2016)
Abstract: The de Broglie relation is revisited in connection with an ab initio relativistic description of particles and waves, which is the same treatment that historically led to this famous relation. In the same context of the Minkowski four-vector formalism, we also discuss the phase and the group velocity of a matter wave, explicitly showing that both transform as ordinary velocities under a Lorentz transformation. We show that such a transformation rule is a necessary condition for the covariance of the de Broglie relation, and stress the pedagogical value of the Einstein-Minkowski-Lorentz relativistic context in the presentation of the de Broglie relation.
