{
  "id": "1709.08835",
  "version": "v1",
  "published": "2017-09-26T05:15:13.000Z",
  "updated": "2017-09-26T05:15:13.000Z",
  "title": "Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials",
  "authors": [
    "Scott E. Hoffmann",
    "Véronique Hussin",
    "Ian Marquette",
    "Yao-Zhong Zhang"
  ],
  "comment": "15 pages, 10 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct the coherent states and Schr\\\"odinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In addition to the coherent states of the annihilation operator, $c$, we form the linearised version, \\tilde{c}, and obtain its coherent states. We find that while the coherent states defined as eigenvectors of the annihilation operator $c$ display only quantum behaviour, those of the linearised version, \\tilde{c}, have position probability densities displaying distinct wavepackets oscillating and colliding in the potential. The collisions are certainly quantum, as interference fringes are produced, but the remaining evolution indicates a classical analogue.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T05:15:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coherent states",
      "non-classical behaviour",
      "displaying distinct wavepackets oscillating",
      "annihilation operator",
      "hermite exceptional orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}