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Pré-Publication, Document De Travail Année : 2023

Scattering Theory in Quantum Mechanical Problems

Résumé

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding scattering matrix and illustrate them on the example of the Schr\"odinger equation. Our goal is to present time-dependent and stationary approaches and to describe the underlying mathematical methods. We also give a sketch of scattering theory for three interacting quantum particles including a difficult problem of the asymptotic completeness of scattering channels. Along with traditional results, we discuss new scattering channels arising for long-range pair interactions.

Dates et versions

hal-03934041 , version 1 (11-01-2023)

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Dmitri Yafaev. Scattering Theory in Quantum Mechanical Problems. 2023. ⟨hal-03934041⟩
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