The Quaternionic Quantum Mechanics

Abstract

A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigen value equation. Each of these components is found to satisfy a generalized damped wave equation. This reduces to the massless Klein-Gordon equation for certain cases. For a plane wave solution the angular frequency is complex. This equation is in agreement with the Einstein energy-momentum formula. The spin of the particle is obtained from the interaction of the particle with the photon field.