{
  "id": "0910.2151",
  "version": "v2",
  "published": "2009-10-12T12:43:00.000Z",
  "updated": "2010-01-12T14:00:17.000Z",
  "title": "Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane",
  "authors": [
    "C. Quesne"
  ],
  "comment": "12 pages, no figure; minor changes; published version",
  "journal": "Mod. Phys. Lett. A 25 (2010) 15-24",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians $H_k$, $k=1$, 2, 3,..., on a plane. The elements of the dihedral group $D_{2k}$ are realized as operators on this plane and used to define some differential-difference operators $D_r$ and $D_{\\varphi}$. The latter serve to construct $D_{2k}$-extended and invariant Hamiltonians $\\chh_k$, from which the starting Hamiltonians $H_k$ can be retrieved by projection in the $D_{2k}$ identity representation space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-12T14:00:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Fd"
    ],
    "keywords": [
      "exchange operator formalism",
      "integrable quantum systems",
      "infinite family",
      "identity representation space",
      "calogero-marchioro-wolfes problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1142/S0217732310032202",
      "journal": "Modern Physics Letters A",
      "year": 2010,
      "volume": 25,
      "number": 1,
      "pages": 15
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010MPLA...25...15Q",
      "inspire": 847600
    }
  }
}