  The list of basic axioms of quantum mechanics as it was formulated by von
Neumann includes only the mathematical formalism of the Hilbert space and its
statistical interpretation. We point out that such an approach is too general
to be considered as the foundation of quantum mechanics. In particular in this
approach any finite-dimensional Hilbert space describes a quantum system.
Though such a treatment might be a convenient approximation it can not be
considered as a fundamental description of a quantum system and moreover it
leads to some paradoxes like Bell's theorem.
  I present a list from seven basic postulates of axiomatic quantum mechanics.
In particular the list includes the axiom describing spatial properties of
quantum system. These axioms do not admit a nontrivial realization in the
finite-dimensional Hilbert space. One suggests that the axiomatic quantum
mechanics is consistent with local realism.
