A New Formulation of Quantum Mechanics

A. I. Arbab, Faisal A. Yassein

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

DOI: 10.4236/jmp.2012.32022                

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.

Keywords

Mathematical Formulation; Quantum Mechanics; Differential Commutator Brackets

Conflicts of Interest

The authors declare no conflicts of interest.

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