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arXiv · 1905.07608

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

Lev Sakhnovich
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Abstract

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.

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Lev Sakhnovich. 2019-05-18. 3D Schr\"odinger equation: scattering operator, scattering amplitude and ergodic property. https://arxiv.org/abs/1905.07608

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