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Open AccessArticle

The Quaternionic Commutator Bracket and Its Implications

by 1,† and 2,*
1
Department of Physics, Faculty of Science, University of Khartoum, P.O. Box 321, Khartoum 11115, Sudan
2
Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123, Muscat 999046, Sultanate of Oman
*
Author to whom correspondence should be addressed.
Current address: Department of Physics, College of Science, Qassim University, Qassim 51452, Saudi Arabia.
Symmetry 2018, 10(10), 513; https://doi.org/10.3390/sym10100513
Received: 11 August 2018 / Revised: 30 September 2018 / Accepted: 9 October 2018 / Published: 16 October 2018
A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. ψ ˜ = ( i c ψ 0 , ψ ) , represents a state of a particle with orbital angular momentum, L = 3 , resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector ψ , points in an opposite direction of L . When a charged particle is placed in an electromagnetic field, 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. View Full-Text
Keywords: commutator bracket; quaternions; magnetic moments; angular momentum; quantum mechanics commutator bracket; quaternions; magnetic moments; angular momentum; quantum mechanics
MDPI and ACS Style

Arbab, A.I.; Al Ajmi, M. The Quaternionic Commutator Bracket and Its Implications. Symmetry 2018, 10, 513. https://doi.org/10.3390/sym10100513

AMA Style

Arbab AI, Al Ajmi M. The Quaternionic Commutator Bracket and Its Implications. Symmetry. 2018; 10(10):513. https://doi.org/10.3390/sym10100513

Chicago/Turabian Style

Arbab, Arbab I.; Al Ajmi, Mudhahir. 2018. "The Quaternionic Commutator Bracket and Its Implications" Symmetry 10, no. 10: 513. https://doi.org/10.3390/sym10100513

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