Abstract: In present work are considered the scheme of
evaluation the transition probability in quantum system. It is based on
path integral representation of transition probability amplitude and its
evaluation by means of a saddle point method, applied to the part of
integration variables. The whole integration process is reduced to
initial value problem solutions of Hamilton equations with a random
initial phase point. The scheme is related to the semiclassical initial
value representation approaches using great number of trajectories. In
contrast to them from total set of generated phase paths only one path
for each initial coordinate value is selected in Monte Karlo process.