We show how the Maxwell's equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. First we derive a quantum equation for a free photon. The three-component complex wavefunction F satisfies two equations, first a Schroedinger-like wave equation and second one a subsidiary condition. The Plank constant appears naturally in the equations as expected from a quantum theory, but can be cancelled out, explaining its absence in Maxwell’s equations. The substitution F=E-iB in the quantum equations, where E and B are the electric and magnetic fields respectively, reproduces exactly the free field Maxwell’s equations. Further we add consistently the sources (electric charge and current densities) to the quantum equations. 

We derive a Lagrangian which reproduces the two quantum equations for the photon wavefunction F with sources. The Lagrangian depends only on the electric and magnetic fields, but not on potentials. Using this Lagrangian we calculate the energy-momentum tensor with a result which confirms the validity of the quantum formalism. We discuss the differences with other formalisms.