On dynamical justification of quantum scattering cross section

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Komech, Alexander^1,2 

[1] Univ Vienna, Fak Math, A-1010 Vienna, Austria

[2] RAS, Inst Informat Transmiss Problems, Moscow, Russia

关键词: Schrodinger equation;    Spherical waves;    Plane waves;    Differential cross section;    Limiting amplitude;    Lippmann-Schwinger equation;   

DOI  :  10.1016/j.jmaa.2015.06.038

来源: Elsevier

【 摘 要 】

We suggest a dynamical justification of quantum differential cross section in the context of long-time transition to stationary regime for the Schrodinger equation. The problem has been stated by Reed and Simon. Our approach is based on spherical incident waves produced by a harmonic source and the long-range asymptotics for the corresponding spherical limiting amplitudes. The main results are as follows: i) the convergence of spherical limiting amplitudes to the limit as the source goes away to infinity, and ii) the proof of the coincidence of the corresponding limit scattering cross section with the universally recognized formula. The main technical ingredients are the Agmon-Jensen-Kato's analytical theory of the Green function, Ikebe's uniqueness theorem for the Lippmann-Schwinger equation, and some refinement of classical long-range asymptotics for the Coulomb potentials. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free