{
  "annotation_id": "11e745a3-113b-4260-8d8d-c86244040908",
  "date_created": "2026-03-02T18:01:00.411000Z",
  "date_modified": "2026-03-02T18:01:00.411000Z",
  "file_hash": "0fb9c3c8f2492f7003be25479e7df7ae521b35ea2e382758cc2e738c2233cd97",
  "private": false,
  "record": {
    "abstract": "The radial Schrodinger equation for a spherically symmetric potential can be\nregarded as a one dimensional classical harmonic oscillator with a\ntime-dependent spring constant. For solving classical dynamics problems,\nsymplectic integrators are well known for their excellent conservation\nproperties. The class of {\\it gradient} symplectic algorithms is particularly\nsuited for solving harmonic oscillator dynamics. By use of Suzuki\u0027s rule for\ndecomposing time-ordered operators, these algorithms can be easily applied to\nthe Schrodinger equation. We demonstrate the power of this class of gradient\nalgorithms by solving the spectrum of highly singular radial potentials using\nKillingbeck\u0027s method of backward Newton-Ralphson iterations.",
    "arxiv_id": "physics/0509229",
    "authors": [
      "Siu A. Chin",
      "Petr Anisimov"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.chem-ph"
    ],
    "doi": "10.1063/1.2150831",
    "title": "Gradient Symplectic Algorithms for Solving the Radial Schrodinger   Equation",
    "url": "https://arxiv.org/abs/physics/0509229"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "991aebba-030b-4eed-9790-0d525f1d3f5d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}