On evolutionary processes in large N quantum mechanics

Equations of motion of large N quantum mechanics are solved for infinite N in the case of unbroken global O(N) symmetry. It is shown that the only correction to the action is a change in the potential. All characteristics of the motion (frequencies of oscillations, times of rolling, a phase portrait etc.) can be computed by means of a classical mechanics for the corrected potential. In particular, a tunneling in the system is absent.