A New Wave Equation of the Electron

Author(s)
Arbab I. Arbab

ABSTRACT

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, *m*_{0}, in the latter by *im*_{0}. 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.

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

KEYWORDS

Dirac Equation, Zitterbewegung, Universal Quantum Wave Equation, Quaternion Quantum Mechanics

Dirac Equation, Zitterbewegung, Universal Quantum Wave Equation, Quaternion Quantum Mechanics

Cite this paper

nullA. 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.

nullA. Arbab, "A New Wave Equation of the Electron,"

References

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[5] A. I. Arbab, “The Quaternionic Quantum Mechanics,” arXiv: 1003.0075v1, 2010..

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[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.