{
  "id": "2205.13204",
  "version": "v1",
  "published": "2022-05-26T07:44:02.000Z",
  "updated": "2022-05-26T07:44:02.000Z",
  "title": "Scattering Theory in Quantum Mechanical Problems",
  "authors": [
    "Dmitri Yafaev"
  ],
  "comment": "A lecture at the les Houches school of physics, September, 2021",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T07:44:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "47A40",
      "81U05",
      "81U10"
    ],
    "keywords": [
      "scattering theory",
      "quantum mechanical problems",
      "three-particle quantum systems",
      "scattering channels",
      "long-range pair interactions"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}