  We discuss the dynamics of single particle by laying a hypothesis that the
Hamilton's principle of stationary action is not exact. We then postulate that
the deviation of the action with sufficiently short time interval from the
stationary action is distributed along a sufficiently long trajectory according
to an exponential law. We show that the dynamics of the ensemble of
trajectories satisfies the Schr\"odinger equation with Born interpretation of
wave function if the average deviation is given by $\hbar/2$ and if two
opposite signs of deviation occur equally probably. The particle thus behaves
as if it is guided by a virtual wave satisfying the Schr\"odinger equation.
