# The Quaternionic Quantum Mechanics - Physics > General Physics

Abstract: A quaternionic wavefunction consisting of real and scalar functions is foundto satisfy the quaternionic momentum eigenvalue equation. Each of thesecomponents are found to satisfy a generalized wave equation of the form$\frac{1}{c^2}\frac{\partial^2\psi 0}{\partial t^2} - abla^2\psi 0+2\frac{m 0}{\hbar}\frac{\partial\psi 0}{\partialt}+\frac{m 0c}{\hbar}^2\psi 0=0$. This reduces to the massless Klein-Gordonequation, if we replace $\frac{\partial}{\partial t}\to\frac{\partial}{\partialt}+\frac{m 0c^2}{\hbar}$. For a plane wave solution the angular frequency iscomplex 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 inagreement with the Einstein energy-momentum formula. The spin of the particleis obtained from the interaction of the particle with the photon field.

Author: Arbab I. Arbab

Source: https://arxiv.org/