{
  "annotation_id": "a74e9106-b2e6-4fba-ae1b-130f3afbc679",
  "date_created": "2026-03-02T18:02:06.634000Z",
  "date_modified": "2026-03-02T18:02:06.634000Z",
  "file_hash": "b6b32a0a13c5c64b30ee53a6492f35517697a3526886ba9344d0e3bf239e84a9",
  "private": false,
  "record": {
    "abstract": "Associated Lam\\\u0027e potentials $V(x)=a(a+1)m\\sn^2(x,m)+b(b+1)m{\\cn^2\n(x,m)}/{\\dn^2(x,m)}$ are used to construct complex, PT-invariant, periodic\npotentials using the anti-isospectral transformation $x \\to ix+\\beta$, where\n$\\beta$ is any nonzero real number. These PT-invariant potentials are defined\nby $V^{PT}(x) \\equiv -V(ix+\\beta)$, and have a different real period from\n$V(x)$. They are analytically solvable potentials with a finite number of band\ngaps, when $a$ and $b$ are integers. Explicit expressions for the band edges of\nsome of these potentials are given. For the special case of the complex\npotential $V^{PT}(x)=-2m\\sn^2(ix+\\beta,m)$, we also analytically obtain the\ndispersion relation. Additional new, solvable, complex, PT-invariant, periodic\npotentials are obtained by applying the techniques of supersymmetric quantum\nmechanics.",
    "arxiv_id": "quant-ph/0402106",
    "authors": [
      "Avinash Khare",
      "Uday Sukhatme"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/j.physleta.2004.03.006",
    "title": "Analytically Solvable PT-Invariant Periodic Potentials",
    "url": "https://arxiv.org/abs/quant-ph/0402106"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5c298405-d3c2-4167-89d0-48a04ab64934",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}