{
  "id": "1404.0968",
  "version": "v1",
  "published": "2014-04-03T15:28:35.000Z",
  "updated": "2014-04-03T15:28:35.000Z",
  "title": "Distributional approach to point interactions in one-dimensional quantum mechanics",
  "authors": [
    "Marcos Calçada",
    "José T. Lunardi",
    "Luiz A. Manzoni",
    "Wagner Monteiro"
  ],
  "comment": "Open Access link: http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstract",
  "journal": "Frontiers in Physics 2:23 (2014)",
  "doi": "10.3389/fphy.2014.00023",
  "categories": [
    "quant-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schr\\\"odinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $\\delta^\\prime$ interaction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T15:28:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional quantum mechanics",
      "distributional approach",
      "one-dimensional quantum mechanical problem",
      "probability current conservation",
      "general point interaction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Frontiers in Physics",
      "year": 2014,
      "month": "Apr",
      "volume": 2,
      "pages": 23
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1288529,
      "adsabs": "2014FrP.....2...23C"
    }
  }
}