A photon density wavefunction

Abstract

Maxwell's equations in the vacuum can be formally cast in the form of Schr\"odinger's equation. Unfortunately, the vector to which this equation directly applies is not a wavefunction: its amplitude squared is not a probability density but the expected energy density of the field. Since we can count photons, there must be a more convincing wavefunction, derived from the EM field, whose amplitude squared is an expected photon density. Mandel proposed the second quantized version of such a wavefunction, but did not link it directly to the EM field. We show how this can be accomplished.