Can Quantum Mechanics explain the Evolution of the Universe?

This manuscript deals with a model of the evolution of an event space represented by the fundamental solution of a N-dimensional generalized Schrodinger equation for free matter. Specifically this solution can be applied to describe the 3D space evolution of the Universe in the forward direction in time. The model which is based on the presented solution is close to the well known Inflation theory, but is nonsingular, does not violate the conservation laws and is finite throughout the whole space at any moment of time. According to this model, the evolution progresses non-uniformly with a positive acceleration. Moreover, the model correctly approaches Hubble's law in the long-time limit. It is also shown that any source functions which describe substance and its physical fields set space topology of the Universe, but do not influence the general dynamics of its evolution.