Incompatibility of the Copenhagen interpretation with quantum mechanics formalism

It is proved the mathematical theorem, that the wave function describes the statistical ensemble of particles, but not a single particle. Supposition, that the wave function describes a single particle appears to be incompatible with formalism of quantum mechanics. Interest to interpretation of quantum mechanics was very large from the very beginning of the quantum mechanics creation up to now. Some scientific journals (Physics Today (1999), Uspechi Fizicheskich Nauk (2002)) organized discussions devoted to problems of quantum measurements and their interpretation. There are scientists [1, 2, 3], which believe that the wave function describes a statistical ensemble. There are scientists [4, 5, 6, 7], which believe that the wave function describes a single particle. There are scientists [8, 9, 10], whose position is intermediate. There is a lot of papers devoted to interpretation of quantum mechanics. All discussions were produced on the verbal level. None of researchers had not set the problem mathematically: Which of interpretations does follow from the quantum mechanics formalism? or in negative form: Which of interpretations is incompatible with the quantum mechanics formalism? Such a statement of the problem seems to be very reasonable. However, the question in such a form was not set. After mathematical solution of this problem any discussion on the verbal level seems to be useless. In this paper we prove a very important theorem, which claims that the wave function may not describe an individual quantum particle. It describes always a statistical ensemble of quantum particles. We shall show, that the action AS for the Schrödinger particle SS (the dynamic system described by the Schrödinger equation) turns into the action AE[Scl] for the statistical ensemble E [Scl] of free classical particles Scl, when the quantum constant ~ → 0. Such a transition is possible only in the case, when the wave function ψ describes a statistical ensemble of quantum particles, but not a single particle.