In this paper, we study the quantum analog of the Aubry–Mather theory from a tomographic point of view. In order to have a well-defined real distribution function for the quantum phase space, which can be a solution for variational action minimizing problems, we reconstruct quantum Mather measures by means of inverse Radon transform and prove that the resulting tomograms, which are fair and non-negative distribution functions, are also solutions of the quantum Mather problem and, in the semi-classical sense, converge to the classical Mather measures.

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