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The paper provides three definitions of the photon position operator basedon: the Poincare group generator, the transversality condition and the helicityoperator. In each case, the correctness of the definition and Hermitianness ofthe operator in the domain of physical states are proven. All considereddefinitions lead to the same form of the position operator in the domain ofphysical states. The components of the photon position operator do not commute,but in analogy to the problem of eigenangular momentum, its eigenstates doexist. Three three-dimensional types of eigenstates of the position operator ofa localized photon are given: on a straight line, on a plane close to a circleand on a plane close to a point. These states are eigenvalues of two or onecomponent of the photon position operator.

Physical unambiguity of the definition of the photon position operator and its special eigenstates