{
  "id": "1702.00851",
  "version": "v1",
  "published": "2017-02-02T22:27:07.000Z",
  "updated": "2017-02-02T22:27:07.000Z",
  "title": "Two interacting particles on the half-line: resolvent and scattering properties",
  "authors": [
    "Sebastian Egger",
    "Joachim Kerner"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we construct the resolvent and analyze scattering properties of the quantum two-body problem introduced in [arXiv:1504.08283] which describes two (distinguishable) particles moving on the half-line under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions the two-body problem is of a non-separable nature. We will discuss the presence of embedded eigenvalues and using the detailed knowledge about the kernel of the resolvent we prove a version of the limiting absorption principle. Furthermore, by an appropriate adaptation of the Lippmann-Schwinger approach we are able to construct generalized eigenfunctions which consequently allow us to establish an explicit expression for the (on-shell) scattering amplitude. An approximation of the scattering amplitude in the weak-coupling limit is also derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-02T22:27:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81U05",
      "81U15",
      "81Q10",
      "81Q50",
      "81Q37",
      "81Q35",
      "81Q80"
    ],
    "keywords": [
      "scattering properties",
      "interacting particles",
      "scattering amplitude",
      "quantum two-body problem",
      "singular two-particle interactions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}