Scattering Theory in Quantum Mechanical Problems
Abstract
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.
Cite
@article{arxiv.2205.13204,
title = {Scattering Theory in Quantum Mechanical Problems},
author = {Dmitri Yafaev},
journal= {arXiv preprint arXiv:2205.13204},
year = {2022}
}
Comments
A lecture at the les Houches school of physics, September, 2021