3D Schr\"odinger equation: scattering operator, scattering amplitude and ergodic property

Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schr"odinger equation. A simple interconnection between the scattering amplitude (stationary case) and scattering operator (dynamical case) is given in the paper. This result is a quantum mechanical analog of the ergodic formulas in the classical mechanics.