Skobeltsyn Institute of Nuclear Physics
Lomonosov Moscow State University

The system of axioms which, on the one hand, is sucient for construction
of the standard mathematical apparatus of quantum mechanics,
and on the other hand, is necessary from the phenomenological point
of view, is described. In a proposed scheme the Hilbert space and linear
operators are only secondary structures of the theory. The elements
of a noncommutative algebra (i.e., the observables) and the functionals
on this algebra serve as the primary components of the theory. The
functionals are associated with the results of a single measurement.