1 October 2013 The Schrödinger description of a single photon
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Abstract
The formulation of the wave function of a single photon has always been in a con ict with the spatial localization of a photon. Lack of the correct treatment for the probability and current density of a single photon resisted self-consistent treatment of the wave function of a single photon. Here we proceed with the construction of the wave function for a single photon that allows us to introduce probability and current density of a single photon. The wave function of a single photon is constructed from the matrix elements of the electric and magnetic elds that couple vacuum state with the Fock state occupied by a single photon. Further we show that the spin of a photon, being projected on the direction of the photon ight propagation, de nes the time evolution of the photon wave function. As the result it can be identi ed with the Hamiltonian of a single photon that establishes Schrodinger equation for a single photon. The Schrodinger description naturally leads to the current and the probability density for a single photon that satis es the continuity equation. The Schrodinger formulation of the Maxwell equations provides a clear physical meaning for the spin of a photon in a similar way to the Dirac equation provides a natural explanation for the spin of an electron.
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Gavriil Shchedrin, Gavriil Shchedrin, } "The Schrödinger description of a single photon", Proc. SPIE 8832, The Nature of Light: What are Photons? V, 883213 (1 October 2013); doi: 10.1117/12.2025969; https://doi.org/10.1117/12.2025969
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