Share This Article:

A New Wave Equation of the Electron

Abstract Full-Text HTML Download Download as PDF (Size:148KB) PP. 1012-1016
DOI: 10.4236/jmp.2011.29121    6,421 Downloads   14,074 Views   Citations
Author(s)    Leave a comment


A new form of Dirac equation of a second order partial differential equation is found. With this wave equation 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Arbab, "A New Wave Equation of the Electron," Journal of Modern Physics, Vol. 2 No. 9, 2011, pp. 1012-1016. doi: 10.4236/jmp.2011.29121.


[1] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, Boston, 1964.
[2] L. Lamata, J. León, T. Sch?tz and E. Solano, “Dirac Equ-ation and Quantum Relativistic Effects in a Single Trapped Ion,” Physical Review Letters, Vol. 98, No. 25, 2007, Article ID: 253005. doi:10.1103/PhysRevLett.98.253005.
[3] D. Walter and H. Gies, “Probing the Quantum Vacuum: Perturbative Effective Action Approach,” Springer Ver-lang, Berlin, 2000..
[4] A. O. Barut and A. J. Bracken, “Zitterbewegung and the Internal Geometry of the Electron,” Physical Review D, Vol. 23, No. 10, 1981, pp. 2454-2463. doi:10.1103/PhysRevD.23.2454.
[5] A. I. Arbab, “The Quaternionic Quantum Mechanics,” arXiv: 1003.0075v1, 2010..
[6] G. Feinberg, “Possibility of Faster-Than-Light Particles,” Physical Review, Vol. 159, No. 5, 1967, pp. 1089-1105. doi:10.1103/PhysRev.159.1089.
[7] J. Ciborowski, “Hypothesis of Tachyonic Neutrinos,” Acta Physicsa Polonica B, Vol. 29, No. 1-2, 1998, pp. 113-121..
[8] R. G. H. Robertson, et al., “Limit on e ν Mass Observation of the β Decay of Molecular Tritium,” Physical Review Letters, Vol. 67, 1991, pp. 957-960. doi:10.1103/PhysRevLett.67.957.
[9] F. Gross, “Relativistic Quantum Mechanics and Field Theory,” John Wiley & Sons, Inc., Hoboken, 1993, p. 97.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.