{
  "annotation_id": "f2ae9c91-4ade-40a1-990a-82a0ccf8bffd",
  "date_created": "2026-03-02T18:01:45.960000Z",
  "date_modified": "2026-03-02T18:01:45.960000Z",
  "file_hash": "2688b13ed7b3044ffea533824996eb62a39e468c9e52983fd67aae83323b9a45",
  "private": false,
  "record": {
    "abstract": "I show that the potential $$V(x,m) = \\big [\\frac{b^2}{4}-m(1-m)a(a+1) \\big\n]\\frac{\\sn^2 (x,m)}{\\dn^2 (x,m)} -b(a+{1/2}) \\frac{\\cn (x,m)}{\\dn^2 (x,m)}$$\nconstitutes a QES band-structure problem in one dimension. In particular, I\nshow that for any positive integral or half-integral $a$, $2a+1$ band edge\neigenvalues and eigenfunctions can be obtained analytically. In the limit of m\ngoing to 0 or 1, I recover the well known results for the QES double\nsine-Gordon or double sinh-Gordon equations respectively. As a by product, I\nalso obtain the boundstate eigenvalues and eigenfunctions of the potential\n$$V(x) = \\big [\\frac{\\beta^2}{4}-a(a+1) \\big ] \\sech^2 x +\\beta(a+{1/2})\\sech\nx\\tanh x$$ in case $a$ is any positive integer or half-integer.",
    "arxiv_id": "quant-ph/0105030",
    "authors": [
      "Avinash Khare"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0375-9601(01)00527-8",
    "journal_ref": "Phys.Lett. A288 (2001) 69-72",
    "title": "A QES Band-Structure Problem in One Dimension",
    "url": "https://arxiv.org/abs/quant-ph/0105030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd78b74d-6c90-4a3f-8129-b40460d48c50",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}