{
  "annotation_id": "bf98f47e-848e-49be-b446-b06d69515045",
  "date_created": "2026-03-02T18:02:07.108000Z",
  "date_modified": "2026-03-02T18:02:07.108000Z",
  "file_hash": "c1c972afd75e6fcd0c58dac938c7b940fbb873e844444e6b276a861f1421a18d",
  "private": false,
  "record": {
    "abstract": "We review the current status of one dimensional periodic potentials and also\npresent several new results. It is shown that using the formalism of\nsupersymmetric quantum mechanics, one can considerably enlarge the limited\nclass of analytically solvable one-dimensional periodic potentials. Further,\nusing the Landen transformations as well as cyclic identities for Jacobi\nelliptic functions discovered by us recently, it is shown that a linear\nsuperposition of Lam\\\u0027e (as well as associated Lam\\\u0027e) potentials are also\nanalytically solvable. Finally, using anti-isospectral transformations, we also\nobtain a class of analytically solvable, complex, PT-invariant, periodic\npotentials having real band spectra.",
    "arxiv_id": "quant-ph/0402206",
    "authors": [
      "Avinash Khare",
      "Uday Sukhatme"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/37/43/002",
    "title": "Periodic Potentials and Supersymmetry",
    "url": "https://arxiv.org/abs/quant-ph/0402206"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a398e33-bc68-4abf-b236-e216899198d3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}