The Quaternionic Quantum Mechanics
Abstract
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form $\frac{1}{c^2}\frac{\partial^2\psi_0}{\partial t^2}  \nabla^2\psi_0+2(\frac{m_0}{\hbar})\frac{\partial\psi_0}{\partial t}+(\frac{m_0c}{\hbar})^2\psi_0=0$. This reduces to the massless KleinGordon equation, if we replace $\frac{\partial}{\partial t}\to\frac{\partial}{\partial t}+\frac{m_0c^2}{\hbar}$. For a plane wave solution the angular frequency is complex and is given by $\vec{\omega}_\pm=i\frac{m_0c^2}{\hbar}\pm c\vec{k} $, where $\vec{k}$ is the propagation constant vector. This equation is in agreement with the Einstein energymomentum formula. The spin of the particle is obtained from the interaction of the particle with the photon field.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 DOI:
 10.48550/arXiv.1003.0075
 arXiv:
 arXiv:1003.0075
 Bibcode:
 2010arXiv1003.0075A
 Keywords:

 Physics  General Physics
 EPrint:
 13 Latex pages, no figures