{
  "annotation_id": "6dd2d8a1-7c60-468f-90d3-713a48a26b48",
  "date_created": "2026-03-02T18:02:10.050000Z",
  "date_modified": "2026-03-02T18:02:10.050000Z",
  "file_hash": "c3f2ad3ab5736f23cac88cdff07870d86f4fc29c7c407ccecec0bdbd4339bbe8",
  "private": false,
  "record": {
    "abstract": "It is shown how using the classical Hamilton-Jacobi equation one can arrive\nat the time-dependent wave equation. Although the former equation was\noriginally used by E.Schroedinger to get the wave equation, we propose a\ndifferent approach. In the first place, we do not use the principle of least\naction and, in addition, we arrive at the time-dependent equation, while\nSchroedinger (in his first seminal paper) used the least action principle and\nobtained the stationary wave equation. The proposed approach works for any\nclassical Hamilton-Jacobi equation. In addition, by introducing information\nloss into the Hamilton-Jacobi equation we derive in an elementary fashion the\nwave equations (ranging from the Shroedinger to Klein-Gordon, to Dirac\nequations). We also apply this technique to a relativistic particle in the\ngravitational field and obtain the respective wave equation. All this supports\n\u0027t Hooft\u0027s proposal about a possibility of arriving at quantum description from\na classical continuum in the presence of information loss.",
    "arxiv_id": "quant-ph/0409018",
    "authors": [
      "A. Granik"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Schroedinger revisited:How the time-dependent wave equation follows from   the Hamilton-Jacobi equation",
    "url": "https://arxiv.org/abs/quant-ph/0409018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "72afc42f-9515-4470-b4cf-166efcd6d4dd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}