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The monochromatic Dirac and polychromatic Titulaer-Glauber quantized fieldtheories (QFTs) of electromagnetism are derived from a photon-energy wavefunction in much the same way that one derives QFT for electrons, that is, byquantization of a single-particle wave function. The photon wave function andits equation of motion are established from the Einstein energy-momentum-massrelation, assuming a local energy density. This yields a theory of photon wavemechanics (PWM). The proper Lorentz-invariant single-photon scalar product isfound to be non-local in coordinate space, and is shown to correspond toorthogonalization of the Titulaer-Glauber wave-packet modes. The wave functionsof PWM and mode functions of QFT are shown to be equivalent, evolving viaidentical equations of motion, and completely describe photonic states. Wegeneralize PWM to two or more photons, and show how to switch between the PWMand QFT viewpoints. The second-order coherence tensors of classical coherencetheory and the two-photon wave functions are shown to propagate equivalently.We give examples of beam-like states, which can be used as photon wavefunctions in PWM, or modes in QFT. We propose a practical mode converter basedon spectral filtering to convert between wave packets and their correspondingbiorthogonal dual wave packets.

Photon wave functions, wave-packet quantization of light, and coherence theory