{
  "annotation_id": "a23cb87d-e247-4a18-965e-04d2d1d5786d",
  "date_created": "2026-03-02T18:02:41.292000Z",
  "date_modified": "2026-03-02T18:02:41.292000Z",
  "file_hash": "69b43ed56d471d1f74c4cb12b75b174aecc3b43ebb8bd013b7195e8d2df89b6f",
  "private": false,
  "record": {
    "abstract": "In the probability representation of quantum mechanics, quantum states are\nrepresented by a classical probability distribution, the marginal distribution\nfunction (MDF), whose time dependence is governed by a classical evolution\nequation. We find and explicitly solve, for a wide class of Hamiltonians, new\nequations for the Green\u0027s function of such an equation, the so-called classical\npropagator. We elucidate the connection of the classical propagator to the\nquantum propagator for the density matrix and to the Green\u0027s function of the\nSchr\\\"odinger equation. Within the new description of quantum mechanics we give\na definition of coherence solely in terms of properties of the MDF and we test\nthe new definition recovering well known results. As an application, the forced\nparametric oscillator is considered . Its classical and quantum propagator are\nfound, together with the MDF for coherent and Fock states.",
    "arxiv_id": "quant-ph/9802030",
    "authors": [
      "V. I. Man\u0027ko",
      "L. Rosa",
      "P. Vitale"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1103/PhysRevA.57.3291",
    "journal_ref": "Phys.Rev. A57 (1998) 3291",
    "title": "Time-Dependent Invariants and Green\u0027s Functions in the Probability   Representation of Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9802030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b8d1b890-3350-4c07-97ad-8b7ff9ed646b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}