In the standard Quantum Mechanics (QM) there exists certain assumption (which I call the von Neuman axiom) stating that an ensemble in the pure state is homogeneous. This means that all members of this ensemble are in the same individual state. Equivalently we can say that each pure state is an individual state (the term individual state means the state of an individual system).
In this note I am going to show that the von Neumann axiom is false. This also means that the standard interpretation of the wave function as the state of the individual system is false.
There are four arguments for this statement.
Thus the von Neumann axiom must be false and we have to look for its modification. I have proposed to choose the opposite possibility: to require that any two different individual states must be orthogonal. I have called this statement the anti-von Neumann axiom and this axiom is the starting point for the axiomatic definition of the modified QM.
We have shown that the ontic interpretation of the wave function cannot be true.