The goal of this work is, the utilization of a method recently developed by the author, in quantum dynamical problems. Main idea is based on the relation between quantum and classical dynamics such that quantum dynamical problems become their classical dynamical counterpaxts when they axe formulated via expectation values of certain operators and the probability density tends to be sharply localized. Expectation values can be expanded into a series in ascending appearence multiplicity of the complement of the projection operator which projects the space spanned by the wave function. This expansion contains fluctuation terms as unknowns besides the expectation values. We construct an infinite set of differential equations. The finite truncations of this set enables us to approximate the quantum dynamics of the system under consideration.