{
  "annotation_id": "3608d218-bd1a-47e2-b7e3-80e99e4d4f8e",
  "date_created": "2026-03-02T18:02:03.646000Z",
  "date_modified": "2026-03-02T18:02:03.646000Z",
  "file_hash": "364fab75bca5d09205d17bc3ef5a664f1881824761db21990da39944f126d849",
  "private": false,
  "record": {
    "abstract": "We obtain the band edge eigenfunctions and the eigenvalues of solvable\nperiodic potentials using the quantum Hamilton - Jacobi formalism. The\npotentials studied here are the Lam{\\\u0027e} and the associated Lam{\\\u0027e} which\nbelong to the class of elliptic potentials. The formalism requires an\nassumption about the singularity structure of the quantum momentum function\n$p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $\np^{2} -i \\hbar \\frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential\nuse is made of suitable conformal transformations, which leads to the\neigenvalues and the eigenfunctions corresponding to the band edges in a simple\nand straightforward manner. Our study reveals interesting features about the\nsingularity structure of $p$, responsible in yielding the band edge\neigenfunctions and eigenvalues.",
    "arxiv_id": "quant-ph/0312041",
    "authors": [
      "S. Sree Ranjani",
      "A. K. Kapoor",
      "P. K. Panigrahi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217732304014197",
    "journal_ref": "Mod. Phys. Lett. A, 19, No. 27, 2047 (2004).",
    "title": "Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic   Potentials through the Quantum Hamilton - Jacobi Formalism",
    "url": "https://arxiv.org/abs/quant-ph/0312041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fe377478-4444-42d7-9240-2e5480517d95",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}