A photon density wavefunction

TL;DR

This paper derives a photon wavefunction from Maxwell's equations, linking the electromagnetic field to a probability density for photon location, addressing a longstanding conceptual gap in quantum optics.

Contribution

It provides a method to obtain a photon wavefunction directly from the EM field, connecting classical electromagnetism with quantum photon descriptions.

Findings

Derived a photon wavefunction from Maxwell's equations.

Linked the wavefunction's amplitude squared to photon density.

Bridged classical EM fields with quantum photon concepts.

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.