{
  "annotation_id": "786ee517-adab-444e-b729-424cb9689033",
  "date_created": "2026-03-02T18:02:06.882000Z",
  "date_modified": "2026-03-02T18:02:06.882000Z",
  "file_hash": "6b3137d90c26950bd03efc0ed8963379c9d9d2b11ef5dfef41e6fb544fde9cfe",
  "private": false,
  "record": {
    "abstract": "Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm\ninterpretation and Nelson\u0027s stochastic interpretation. It is shown that the\nusual route to establishing the validity of such interpretations, via a\ndecomposition of the Schroedinger equation into a continuity equation and a\nmodified Hamilton-Jacobi equation, fails for some quantum states. A very simple\nexample is provided by a quantum particle in a box, described by a wavefunction\ninitially uniform over the interior of the box. For this example there is no\ncorresponding continuity or modified Hamilton-Jacobi equation, and the\nspacetime dependence of the wavefunction has a known fractal structure.\nExamples with finite average energies are also constructed.",
    "arxiv_id": "quant-ph/0406054",
    "authors": [
      "Michael J. W. Hall"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/37/40/015",
    "journal_ref": "J. Phys. A 37 (2004) 9549 (www.iop.org)",
    "title": "Incompleteness of trajectory-based interpretations of quantum mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0406054"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2eedda23-44c7-4eec-9178-db82a80b71ea",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}