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We present a study on linear canonical transformation in the framework of aphase space representation of quantum mechanics that we have introduced in ourprevious work [1]. We begin with a brief recall about the so called phase spacerepresentation. We give the definition of linear canonical transformation withthe transformation law of coordinate and momentum operators. We establishsuccessively the transformation laws of mean values, dispersions, basis stateand wave functions.Then we introduce the concept of isodispersion linearcanonical transformation.

Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics