{
  "annotation_id": "6d99a074-7792-4a5b-a982-cb4a0e9c48ec",
  "date_created": "2026-03-02T18:01:14.640000Z",
  "date_modified": "2026-03-02T18:01:14.640000Z",
  "file_hash": "42cb980fe9c1b7be1955620865d6020b25199b937f9e3516225516abebeb6f68",
  "private": false,
  "record": {
    "abstract": "A new numerical treatment in the Crank-Nicholson method with the imaginary\ntime evolution operator is presented in order to solve the Schr\\\"{o}dinger\nequation. The original time evolution technique is extended to a new operator\nthat provides a systematic way to calculate not only eigenvalues of ground\nstate but also of excited states. This new method systematically produces\neigenvalues with accuracies of eleven digits with the Cornell potential that\ncovers non-perturbative regime. An absolute error estimation technique based on\na power counting rule is implemented. This method is examined with exactly\nsolvable problems and produces the numerical accuracy down to 10$^{-11}$.",
    "arxiv_id": "physics/0609176",
    "authors": [
      "Daekyoung Kang",
      "E. Won"
    ],
    "categories": [
      "physics.comp-ph",
      "hep-ph",
      "physics.atom-ph"
    ],
    "doi": "10.1016/j.jcp.2007.11.028",
    "journal_ref": "J.Comput.Phys.227:2970-2976,2008",
    "title": "Precise Numerical Solutions of Potential Problems Using Crank-Nicholson   Method",
    "url": "https://arxiv.org/abs/physics/0609176"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8019ff9e-1b6a-41ee-bf83-92dd7e491683",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}