{
  "id": "1601.05359",
  "version": "v1",
  "published": "2016-01-20T18:16:46.000Z",
  "updated": "2016-01-20T18:16:46.000Z",
  "title": "Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach",
  "authors": [
    "V. G. Ibarra-Sierra",
    "J. C. Sandoval-Santana",
    "J. L. Cardoso",
    "A. Kunold"
  ],
  "comment": "17 pages, 3 tables",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-20T18:16:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebraic approach",
      "time evolution",
      "evolution operator",
      "generalized two-dimensional quadratic hamiltonian",
      "heisenberg picture position"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160105359I"
    }
  }
}