Relativistic Schrodinger equation and probability currents for quantum particles

In this work, we face the problem of quantizing the relativistic Hamiltonian of a quantum particle (electrons, photons, etc.). In tempered distribution state spaces, we nd the natural way to dene the relativistic Hamiltonian operator and its associated Schrodinger equation. We, then, deduce the equivalent continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine the possible probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrodinger equation and probability flux continuity equations.