{
  "annotation_id": "bfda3b8d-f43a-48f4-8394-61fdf0ac5d9b",
  "date_created": "2026-03-02T18:02:34.234000Z",
  "date_modified": "2026-03-02T18:02:34.234000Z",
  "file_hash": "c67d1f7f5e31d5fbed3d922e9b3bd9b9e4fc930cc163bbe76aad791b1fee517a",
  "private": false,
  "record": {
    "abstract": "In a stationary case and for any potential, we solve the three-dimensional\nquantum Hamilton-Jacobi equation in terms of the solutions of the corresponding\nSchrodinger equation. Then, in the case of separated variables, by requiring\nthat the conjugate momentum be invariant under any linear transformation of the\nsolutions of the Schrodinger equation used in the reduced action, we clearly\nidentify the integration constants successively in one, two and three\ndimensions. In each of these cases, we analytically establish that the quantum\nHamilton-Jacobi equation describes microstates not detected by the Schrodinger\nequation in the real wave function case.",
    "arxiv_id": "quant-ph/0701159",
    "authors": [
      "A. Bouda",
      "A. Mohamed Meziane"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "journal_ref": "Int. J. Theo. Phys. 45 (2006) 1323",
    "title": "The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates",
    "url": "https://arxiv.org/abs/quant-ph/0701159"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55bfa7b3-69f3-48d5-8794-6669573115cd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}