A quaternion expression for the quantum mechanical probability and current densities

Abstract

A simple quaternion expression is proposed for the quantum mechanical four-current of a single particle. It is shown that the equation of continuity is obeyed and the behaviour under a Lorentz transformation is correct. The expression is almost equivalent to that emanating from the Dirac theory. It differs, however, from those of other authors who have considered the quaternion formulation of relativistic quantum mechanics.