Relativistic Derivations of de Broglie and Planck-Einstein Equations

Abstract

Special Relativity sets tight constraints on the form of the possible relations between the four-momentum of a particle and the wave four-vector. In fact, we demonstrate that there is just one way, according to Special Relativity, to relate the energy and the momentum of a corpuscle with the characteristics of a plane wave, frequency and wave vector, if the momentum has to flow in the same direction of the wave propagation: the laws must be of direct proportionality like de Broglie and Planck-Einstein equations.