A New Wave Equation of the Electron
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Abstract
A new form of Dirac equation of a second order partial differential equation is found. With this wave equation the quivering motion (<i>Zitterbewegung</i>) 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, <i>m<sub>0</sub></i>, in the latter by <i>im<sub>0</sub></i>. 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.
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