Orthogonal polynomials in phase space and classical analogs to quantum eigenstates with an application to the transmission flux for the potential step

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Abstract
We introduce a set of orthogonal polynomials in phase space with similar properties, and which can be reduced to the usual Hermite polynomials. Based on these polynomials, we develop a method that allows the finding of classical analogs to quantum eigenstates. This method is applied to the free particle scattered by a potential step and the transmission flux is calculated and compared with the quantum one.