{
  "id": "1003.4129",
  "version": "v1",
  "published": "2010-03-22T11:05:07.000Z",
  "updated": "2010-03-22T11:05:07.000Z",
  "title": "Asymptotic Expansion for the Wave Function in a one-dimensional Model of Inelastic Interaction",
  "authors": [
    "Domenico Finco",
    "Alessandro Teta"
  ],
  "comment": "23 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average velocity $\\pm v_0$ while the oscillator is in its ground state. In a suitable scaling limit, corresponding for the test particle to a semi-classical regime with small energy exchange with the oscillator, we give a complete asymptotic expansion of the wave function of the system in both cases $R_0 <a$ and $R_0 >a$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-22T11:05:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q05",
      "03.65.Ge",
      "03.65.Sq"
    ],
    "keywords": [
      "wave function",
      "one-dimensional model",
      "inelastic interaction",
      "test particle",
      "small energy exchange"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3549587",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Feb",
      "volume": 52,
      "number": 2,
      "pages": 2103
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JMP....52b2103F"
    }
  }
}