{
  "annotation_id": "f7090970-bd91-410c-9bc7-10576480383e",
  "date_created": "2026-03-02T18:00:56.434000Z",
  "date_modified": "2026-03-02T18:00:56.434000Z",
  "file_hash": "2a0e317100c4fce4aff569ad1dfba81b9b6744de22c5d08dedeb27bbe7956d46",
  "private": false,
  "record": {
    "abstract": "A simple position probability density formulation is presented for the motion\nof a particle in a spherically symmetric potential. The approach provides an\nalternative to Newtonian methods for presentation in an elementary course, and\nrequires only elementary algebra and one tabulated integral. The method is\napplied to compute the distributions for the Kepler-Coulomb and isotropic\nharmonic oscillator potentials. Formulas are also deduced for the average\nvalues for powers of the radial coordinate, and applied to describe\nperturbations to these systems. The classical results are also compared with\nquantum mechanical calculations using the Einstein-Brillouin-Keller\nsemiclassical quantization.",
    "arxiv_id": "physics/0501111",
    "authors": [
      "Lorenzo J. Curtis",
      "David G. Ellis"
    ],
    "categories": [
      "physics.ed-ph"
    ],
    "title": "Classical position probability densities for spherically symmetric   potentials",
    "url": "https://arxiv.org/abs/physics/0501111"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e29ff334-979c-4335-8bf6-aaa14bedaea9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}