The quaternionic commutator bracket and its implications

Arbab I. Arbab; Mudhahir Al-Ajmi

doi:10.3390/sym10100513

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arXiv · 1401.5315

The quaternionic commutator bracket and its implications

Arbab I. Arbab·Mudhahir Al-Ajmi

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Abstract

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, \emph{viz.} $\widetilde{\psi}=(\frac{i}{c}\,\psi_0\,,\vec{\psi})$, represents a state of a particle with orbital angular momentum, $L=3\,\hbar$, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector $\vec{\psi}$, points along the direction of $\vec{L}$. When a charged particle is placed in an electromagnetic fields the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov-Bohm and Aharonov-Casher effects.

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Arbab I. Arbab, Mudhahir Al-Ajmi. 2014-01-21. The quaternionic commutator bracket and its implications. https://doi.org/10.3390/sym10100513

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