Single-Frequency Quaternion Wave Equation

Abstract

Using Maxwell's equations for a single-frequency quaternion, wave equations for magnetic and electrical intensity are obtained. It is shown that waves propagate in space in the form of circulation of these intensities. Since Maxwell's equations for the quaternion contain scalar parts in the form of electric charges of electrons and their spins (rotors), then along with magnetic and electric waves there are also electric and magnetic fluxes in the form of charges and rotors. The values of charge and rotor densities are calculated from magnetic and electrical intensities by means of their scalar product with the Hamiltonian operator in matrix representation.

According to Faraday's law, it is known that the derivatives of magnetic intensity correspond to electrical intensity, therefore magnetic and electrical waves can be considered as electromagnetic.