The quaternionic commutator bracket and its implications
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2014
- DOI:
- 10.48550/arXiv.1401.5315
- arXiv:
- arXiv:1401.5315
- Bibcode:
- 2014arXiv1401.5315A
- Keywords:
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- Physics - General Physics;
- Quantum Physics
- E-Print:
- 8 pages