A New Wave Equation of the Electron

Abstract

A new form of Dirac equation of a second order partial differential equation is found. With this wave equa- tion the quivering motion (Zitterbewegung) is satisfactorily explained. A quaternionic analogue of Dirac equation is presented and compared with the ordinary Dirac equation. The two equations become the same if we replace the particle rest mass, m0, in the latter by im0. New space and time transformations in which these two equations represent a massless particle are found. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. The electron is found to be represented by a superposition of two waves with a group velocity equals to speed of light in vacuum