On the dynamics of the quantum states set for a system with degenerated Hamiltonian

We study the sequence of regularizing Cauchy problem as the elliptic regularization of Cauchy problem for Schrodinger equation with discontinuous and degenerated coefficients. The necessary and sufficient condition of the convergence of the regularizing dynamical semigroups sequence are presented. If the convergence is impossible then divergent sequence of the regularizing quantum states is considered as the stochastic process on the measurable space of regularizing parameter endowing with finite additive measure. The expectation of this stochastic process defines the averaging trajectory in the space of quantum states. It was obtained the condition on the finite additive measure such, that averaging trajectory can be defined by its values in two instants with the help of solving the variational problems.