{
  "annotation_id": "bd75506a-20ce-4073-bff3-fd8b6a1dd5f5",
  "date_created": "2026-03-02T18:02:23.726000Z",
  "date_modified": "2026-03-02T18:02:23.726000Z",
  "file_hash": "9d0f26adda86723ba41c7336906cd240f1e8e207635be7c6eac34277e621ad86",
  "private": false,
  "record": {
    "abstract": "We derive a classical Schrodinger type equation from the classical Liouville\nequation in phase space. The derivation is based on a Wigner type Fourier\ntransform of the classical phase space probability distribution, which depends\non an arbitrary constant $\\alpha$ with dimension of action. In order to achieve\nthis goal two requirements are necessary: 1) It is assumed that the classical\nprobability amplitude $\\Psi(x,t)$ can be expanded in a complete set of\nfunctions $\\Phi_n(x)$ defined in the configuration space; 2) the classical\nphase space distribution $W(x,p,t)$ obeys the Liouville equation and is a real\nfunction of the position, the momentum and the time. We show that the constant\n$\\alpha$ appearing in the Fourier transform of the classical phase space\ndistribution, and also in the classical Schrodinger type equation, has its\norigin in the spectral distribution of the vacuum zero-point radiation, and is\nidentified with the Planck\u0027s constant $\\hbar$.",
    "arxiv_id": "quant-ph/0512049",
    "authors": [
      "Edelver Carnovali Jr.",
      "Humberto M. Franca"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the conection between the Liouville equation and the Schrodinger   equation",
    "url": "https://arxiv.org/abs/quant-ph/0512049"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d22c8ecc-f0ab-4782-b7db-8820aa5052af",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}