Integrals of motion and symmetry of quantum systems

Two notions: a) motion integral of a physical system, b) physical system symmetry - are analyzed and relation of these notions is elucidated. The consideration is performed within the framework of quantum systems described with the Schroedinger equation although it is true also for classical systems and for relativistic systems described with the Dirac equation, for example. It was proved that motion integrals and the Green function are connected with each other by a series of relations. The Green function in the coordinate representation is the eigenvalue solution of a set of equations