Approximation of the evolution operator by expectations of functionals of sums of independent random variables

A method of probabilistic approximation of the operator $e^{-itH}$, where $H = -\frac{1}{2}\,\frac{d^2}{dx^2}+V(x)$, $V\in L_\infty(\mathbf R)$, in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables.