  The Heisenberg picture of the minisuperspace model is considered. The
suggested quantization scheme interprets all the observables including the
Universe scale factor as the (quasi)Heisenberg operators. The operators arise
as a result of the re-quantization of the Heisenberg operators that is required
to obtain the hermitian theory. It is shown that the DeWitt constraint H=0 on
the physical states of the Universe does not prevent a time-evolution of the
(quasi)Heisenberg operators and their mean values. Mean value of an observable,
which is singular in a classical theory, is also singular in a quantum case.
The (quasi)Heisenberg operator equations are solved in an analytical form in a
first order on the interaction constant for the quadratic inflationary
potential. Operator solutions are used to evaluate the observables mean values
and dispersions. A late stage of the inflation is considered numerically in the
framework of the Wigner-Weyl phase-space formalism. It is found that the
dispersions of the observables do not vanish at the inflation end.
