{
  "id": "1010.5525",
  "version": "v3",
  "published": "2010-10-26T21:30:28.000Z",
  "updated": "2011-07-01T17:13:56.000Z",
  "title": "Harmonic states for the free particle",
  "authors": [
    "Julio Guerrero",
    "Francisco F. López-Ruiz",
    "Victor Aldaya",
    "Francisco Cossio"
  ],
  "comment": "21 pages, 3 figures. Title changed, content added, references added",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Different families of states, which are solutions of the time-dependent free Schr\\\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-07-01T17:13:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free particle",
      "harmonic states",
      "paraxial wave optics",
      "quantum arnold transformation",
      "time-dependent free"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/44/44/445307",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Nov",
      "volume": 44,
      "pages": 445307
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44R5307G"
    }
  }
}