{
  "annotation_id": "b092dc0c-4e87-4023-975a-e88195074d10",
  "date_created": "2026-03-02T18:01:38.973000Z",
  "date_modified": "2026-03-02T18:01:38.973000Z",
  "file_hash": "1ae5288a48f517081a60c6a96e3d9bc2efdbccee245bf772002d3a0663c7427e",
  "private": false,
  "record": {
    "abstract": "The radial momentum operator in quantum mechanics is usually obtained through\ncanonical quantization of the (symmetrical form of the) classical radial\nmomentum. We show that the well known connection between the Hamiltonian of a\nfree particle and the radial momentum operator $\\hat{H}=\\hat{P}_{r}^2/2m+\n$\\hat{L}^2$}/2mr^{2}$ is true only in one or three dimensions. In general, an\nextra term of the form $\\hbar^{2}(n-1)(n-3)/ 2m \\cdot 4r^{2}$ has to be added\nto the Hamiltonian.",
    "arxiv_id": "quant-ph/0009046",
    "authors": [
      "Gil Paz"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0143-0807/22/4/308",
    "journal_ref": "European Journal of Physics Vol. 22 no. 4 p. 337",
    "title": "On the connection between the radial momentum operator and the   Hamiltonian in n dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0009046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "72ded19c-ceca-4982-9800-1e6419efcde2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}