{
  "id": "math-ph/0005012",
  "version": "v1",
  "published": "2000-05-10T13:10:31.000Z",
  "updated": "2000-05-10T13:10:31.000Z",
  "title": "Conjecture on the Interlacing of Zeros in Complex Sturm-Liouville Problems",
  "authors": [
    "C. M. Bender",
    "S. Boettcher",
    "V. M. Savage"
  ],
  "comment": "13 pages, RevTex, 6 figures, for related papers, see http://www.physics.emory.edu/faculty/boettcher/#PT",
  "journal": "J.Math.Phys. 41 (2000) 6381",
  "doi": "10.1063/1.1288247",
  "categories": [
    "math-ph",
    "cond-mat",
    "hep-lat",
    "hep-th",
    "math.MP"
  ],
  "abstract": "The zeros of the eigenfunctions of self-adjoint Sturm-Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm-Liouville problem associated with the Schrodinger equation for a non-Hermitian PT-symmetric Hamiltonian, completeness and interlacing of zeros have never been examined. This paper reports a numerical study of the Sturm-Liouville problems for three complex potentials, the large-N limit of a -(ix)^N potential, a quasi-exactly-solvable -x^4 potential, and an ix^3 potential. In all cases the complex zeros of the eigenfunctions exhibit a similar pattern of interlacing and it is conjectured that this pattern is universal. Understanding this pattern could provide insight into whether the eigenfunctions of complex Sturm-Liouville problems form a complete set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-05-10T13:10:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "self-adjoint sturm-liouville eigenvalue problems interlace",
      "interlacing",
      "complex sturm-liouville problems form",
      "non-hermitian pt-symmetric hamiltonian"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 547094
    }
  }
}