{
  "id": "0805.4024",
  "version": "v1",
  "published": "2008-05-27T19:59:33.000Z",
  "updated": "2008-05-27T19:59:33.000Z",
  "title": "Hamiltonian Systems Inspired by the Schrödinger Equation",
  "authors": [
    "Vasyl Kovalchuk",
    "Jan Jerzy Slawianowski"
  ],
  "comment": "This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 4 (2008), 046, 9 pages",
  "doi": "10.3842/SIGMA.2008.046",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special cases for the free evolution of the wave function with fixed G and the pure dynamics of G are calculated. The usual, first- and second-order modified Schr\\\"odinger equations are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-27T19:59:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian systems",
      "schrödinger equation",
      "wave function",
      "n-level quantum system",
      "scalar product"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2008,
      "month": "May",
      "volume": 4,
      "pages": "046"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008SIGMA...4..046K"
    }
  }
}