A wave function for single- and many-photon states is defined by associating photons with different momenta with different spectral and polarization components of the classical, generally complex, electromagnetic field that propagates in a definite direction. When each spectral component of the classical field is scaled to the square root of the photon energy, the appropriately normalized photon wave function acquires the desired interpretation of probability density amplitude, in contradistinction to the Riemann–Silberstein wave function that can be considered the amplitude of the photon probability energy density.
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