{
  "annotation_id": "8d31c5ba-b482-48d9-a4f8-f25fffdd20bf",
  "date_created": "2026-03-02T18:01:45.960000Z",
  "date_modified": "2026-03-02T18:01:45.960000Z",
  "file_hash": "a21540477cad9cbabfe7f7c126616ff14597c469dc8f12148bd88e690b65d578",
  "private": false,
  "record": {
    "abstract": "Applying certain known theorems about one-dimensional periodic potentials, we\nshow that the energy spectrum of the associated Lam\\\u0027{e} potentials\n$$a(a+1)m~{\\rm sn}^2(x,m)+b(b+1)m~{\\rm cn}^2(x,m)/{\\rm dn}^2(x,m)$$ consists of\na finite number of bound bands followed by a continuum band when both $a$ and\n$b$ take integer values. Further, if $a$ and $b$ are unequal integers, we show\nthat there must exist some zero band-gap states, i.e. doubly degenerate states\nwith the same number of nodes. More generally, in case $a$ and $b$ are not\nintegers, but either $a + b$ or $a - b$ is an integer ($a \\ne b$), we again\nshow that several of the band-gaps vanish due to degeneracy of states with the\nsame number of nodes. Finally, when either $a$ or $b$ is an integer and the\nother takes a half-integral value, we obtain exact analytic solutions for\nseveral mid-band states.",
    "arxiv_id": "quant-ph/0105044",
    "authors": [
      "Avinash Khare",
      "Uday Sukhatme"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1416487",
    "journal_ref": "J.Math.Phys. 42 (2001) 5652-5664",
    "title": "Some Exact Results for Mid-Band and Zero Band-Gap States of Associated   Lame Potentials",
    "url": "https://arxiv.org/abs/quant-ph/0105044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4df05df2-81dc-44a1-927e-1138c017ad82",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}