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I'm now reading the section which introduces about Wigner function in the Optics textbook. What I want to ask is that I've got a problem for understand the converting process of these two equations. Following the context of the book, It says that by solving the former equation as a Wigner distribution function then We can get the latter one. (I mistake for wrote, a commutator of the operator must be -1)

Can anyone explain the solution process?

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