{
  "id": "0812.5055",
  "version": "v2",
  "published": "2008-12-30T11:53:17.000Z",
  "updated": "2009-11-18T14:11:58.000Z",
  "title": "Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics",
  "authors": [
    "J. J. Sławianowski",
    "V. Kovalchuk"
  ],
  "comment": "51 pages",
  "journal": "Reports on Mathematical Physics, vol. 65, no. 1, 2010, pp. 29-76.",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Considered is the Schr\\\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of \"mechanics\" with singular Lagrangians, effectively treatable within the framework of Dirac formalism. We discuss also some modified \"Schr\\\"odinger\" equations involving second-order time derivatives and introduce a kind of non-direct, non-perturbative, geometrically-motivated nonlinearity based on making the scalar product a dynamical quantity. There are some reasons to expect that this might be a new way of describing open dynamical systems and explaining some quantum \"paradoxes\".",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-18T14:11:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian systems",
      "second-order tensors",
      "quantum mechanics",
      "related equations",
      "nonlinearity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.5055S"
    }
  }
}