{
  "annotation_id": "109deca2-0ab9-4391-96c8-1b0c56ea9c0b",
  "date_created": "2026-03-02T18:00:32.606000Z",
  "date_modified": "2026-03-02T18:00:32.606000Z",
  "file_hash": "c87381eeedf18025b4c3702e24ad3fb140b1afd7a0f1ebc0ad6014bcbd70139f",
  "private": false,
  "record": {
    "abstract": "We show that the method of splitting the operator ${\\rm e}^{\\epsilon(T+V)}$\nto fourth order with purely positive coefficients produces excellent algorithms\nfor solving the time-dependent Schr\\\"odinger equation. These algorithms require\nknowing the potential and the gradient of the potential. One 4th order\nalgorithm only requires four Fast Fourier Transformations per iteration. In a\none dimensional scattering problem, the 4th order error coefficients of these\nnew algorithms are roughly 500 times smaller than fourth order algorithms with\nnegative coefficient, such as those based on the traditional Ruth-Forest\nsymplectic integrator. These algorithms can produce converged results of\nconventional second or fourth order algorithms using time steps 5 to 10 times\nas large. Iterating these positive coefficient algorithms to 6th order also\nproduced better converged algorithms than iterating the Ruth-Forest algorithm\nto 6th order or using Yoshida\u0027s 6th order algorithm A directly.",
    "arxiv_id": "physics/0012017",
    "authors": [
      "Siu A. Chin",
      "C. -R. Chen"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.chem-ph"
    ],
    "doi": "10.1063/1.1362288",
    "title": "Fourth Order Gradient Symplectic Integrator Methods for Solving the   Time-Dependent Schr\\\"odinger Equation",
    "url": "https://arxiv.org/abs/physics/0012017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1de44fa3-43ce-4ab2-9c8d-c1b1b8322595",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}