{
  "id": "1104.4042",
  "version": "v2",
  "published": "2011-04-20T14:40:07.000Z",
  "updated": "2011-04-26T19:58:59.000Z",
  "title": "Proof of non-extremal nature of excited-state energies in nonrelativistic quantum mechanics with the use of constrained derivatives",
  "authors": [
    "Tamas Gal"
  ],
  "comment": "15 pages; determination of Morse index added",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "With the use of a second derivative test based on constrained second derivatives, a proof is given that excited states in nonrelativistic quantum mechanics are saddle points of the energy expectation value, and is shown, further, how to determine their Morse index.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-26T19:58:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonrelativistic quantum mechanics",
      "excited-state energies",
      "non-extremal nature",
      "constrained derivatives",
      "energy expectation value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4042G"
    }
  }
}