Relativistic Derivations of de Broglie and Planck-Einstein Equations

Abstract

We show how Special Relativity sets tight constraints on the form of possible relations that may exist between the four-momentum of a particle and the wave four-vector. More specifically, we demonstrate that there is just one way, according to Special Relativity, to relate the finite energy and momentum of a corpuscle with the characteristics of a plane wave, frequency, wave vector and amplitude: that is by laws of direct proportionality like de Broglie equation and Planck-Einstein equation.