The quaternionic commutator bracket and its implications

Abstract

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, \emph{viz.} $\tilde{\psi }=(\frac{i}{c}{\psi }_0,\vec{\psi })$, represents a state of a particle with orbital angular momentum, $L=3\hslash$, 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.

8 pages

References in corpus (2)

• The Quaternionic Quantum Mechanics
• Derivation of Dirac, Klein-Gordon, Schrodinger, Diffusion and quantum heat transport equations from a universal quantum wave equation