{
  "id": "2012.10321",
  "version": "v1",
  "published": "2020-12-18T16:05:17.000Z",
  "updated": "2020-12-18T16:05:17.000Z",
  "title": "Moments and saturation properties of eigenstates",
  "authors": [
    "Martin Bojowald",
    "Jonathan Guglielmon",
    "Martijn van Kuppeveld"
  ],
  "comment": "30 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic oscillator, together with a perturbative treatment of anharmonic systems. In this process, a collection of inequalities is uncovered which amount to uncertainty relations for higher-order moments saturated by the harmonic-oscillator excited states. Similar saturation properties hold for anharmonic systems order by order in perturbation theory. The new method, based on recurrence relations for moments of a state combined with positivity conditions, is therefore able to show new physical features.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-18T16:05:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenstates",
      "similar saturation properties hold",
      "systematic algebraic derivation",
      "anharmonic systems order",
      "wave functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}