A New Formulation of Quantum Mechanics

Affiliation(s)

Department of Physics, Faculty of Science, University of Khartoum, Khartoum, Sudan.

Department of Physics, Faculty of Science, Alneelain University, Khartoum, Sudan.

Department of Physics, Faculty of Science, University of Khartoum, Khartoum, Sudan.

Department of Physics, Faculty of Science, Alneelain University, Khartoum, Sudan.

ABSTRACT

A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and Schrodinger probability density while keeping the Klein-Gordon and Schrodinger current unaltered. We have found time and space transformations under which Dirac’s equation is invariant. The invariance of Maxwell’s equations under these transformations shows that the electric and magnetic fields of a moving charged particle are perpendicular to the velocity of the propagating particle. This formulation agrees with the quaternionic formulation recently developed by Arbab.

A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and Schrodinger probability density while keeping the Klein-Gordon and Schrodinger current unaltered. We have found time and space transformations under which Dirac’s equation is invariant. The invariance of Maxwell’s equations under these transformations shows that the electric and magnetic fields of a moving charged particle are perpendicular to the velocity of the propagating particle. This formulation agrees with the quaternionic formulation recently developed by Arbab.

Cite this paper

A. Arbab and F. Yassein, "A New Formulation of Quantum Mechanics,"*Journal of Modern Physics*, Vol. 3 No. 2, 2012, pp. 163-169. doi: 10.4236/jmp.2012.32022.

A. Arbab and F. Yassein, "A New Formulation of Quantum Mechanics,"

References

[1] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Me- chanics,” McGraw-Hill, New York, 1964.

[2] L. D. Landau and E. M. Liftshiz, “Quantum Mechanics,” 3rd Edition, Pergamon Press, Oxford, 1977.

[3] V. B. Berestetskii, L. P. Pitaevskii and E. M. Lifshitz, “Quantum Electrodynamics,” 2nd Edition, Vol. 4, Else- vier, Amsterdam, 1982.

[4] A. I. Arbab and Z. Satti, “On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave,” Progress in Physics, Vol. 2, No. 8, 2009, pp. 8-13.

[5] A. I. Arbab and H. M. Widatallah, “The Generalized Con- tinuity Equations,” Chinese Physics Letters, Vol. 27, No. 8, 2010, Article ID 084703. doi:10.1088/0256-307X/27/8/084703

[6] A. I. Arbab and F. A. Yassein, “A New Formulation of Electromagnetism,” Journal of Electromagnetic Analysis and Applications, Vol. 2, No. 8, 2010, p. 457. doi:10.4236/jemaa.2010.28060

[7] A. I. Arbab, “A Quaternionic Quantum Mechanics,” Applied Physics Research, Vol. 3, No. 2, 2011, p. 160.

[8] P. G. Tait, “An Elementary Treatise on Quaternions,” 2nd Edition, Cambridge University Press, Cambridge, 1873.

[9] H. F. Harmuth, T. W. Barrett and B. Meffert, “Modified Maxwell Equations in Quantum Electrodynamics,” World Scientific, River Edge, 2001. doi:10.1142/9789812799654

[10] G. Feinberg, “Possibility of Faster-Than-Light Particles,” Physical Reviews, Vol. 159, No. 5, 1967, pp. 1089-1105. doi:10.1103/PhysRev.159.1089

[11] J. Ciborowski, “Hypothesis of Tachyonic Neutrinos,” Acta Physicsa Polonica B, Vol. 29, No. 1-2, 1998, pp. 113-121.

[12] J. D. Jackson, “Classical Electrodynamics,” 2nd Edition, Wiley, New York, 1975.

[13] F. Zbigniew, “Lecture Notes in Electromagnetic Theory,” University of Queensland, Brisbane, 2005.

[1] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Me- chanics,” McGraw-Hill, New York, 1964.

[2] L. D. Landau and E. M. Liftshiz, “Quantum Mechanics,” 3rd Edition, Pergamon Press, Oxford, 1977.

[3] V. B. Berestetskii, L. P. Pitaevskii and E. M. Lifshitz, “Quantum Electrodynamics,” 2nd Edition, Vol. 4, Else- vier, Amsterdam, 1982.

[4] A. I. Arbab and Z. Satti, “On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave,” Progress in Physics, Vol. 2, No. 8, 2009, pp. 8-13.

[5] A. I. Arbab and H. M. Widatallah, “The Generalized Con- tinuity Equations,” Chinese Physics Letters, Vol. 27, No. 8, 2010, Article ID 084703. doi:10.1088/0256-307X/27/8/084703

[6] A. I. Arbab and F. A. Yassein, “A New Formulation of Electromagnetism,” Journal of Electromagnetic Analysis and Applications, Vol. 2, No. 8, 2010, p. 457. doi:10.4236/jemaa.2010.28060

[7] A. I. Arbab, “A Quaternionic Quantum Mechanics,” Applied Physics Research, Vol. 3, No. 2, 2011, p. 160.

[8] P. G. Tait, “An Elementary Treatise on Quaternions,” 2nd Edition, Cambridge University Press, Cambridge, 1873.

[9] H. F. Harmuth, T. W. Barrett and B. Meffert, “Modified Maxwell Equations in Quantum Electrodynamics,” World Scientific, River Edge, 2001. doi:10.1142/9789812799654

[10] G. Feinberg, “Possibility of Faster-Than-Light Particles,” Physical Reviews, Vol. 159, No. 5, 1967, pp. 1089-1105. doi:10.1103/PhysRev.159.1089

[11] J. Ciborowski, “Hypothesis of Tachyonic Neutrinos,” Acta Physicsa Polonica B, Vol. 29, No. 1-2, 1998, pp. 113-121.

[12] J. D. Jackson, “Classical Electrodynamics,” 2nd Edition, Wiley, New York, 1975.

[13] F. Zbigniew, “Lecture Notes in Electromagnetic Theory,” University of Queensland, Brisbane, 2005.