{
  "annotation_id": "79179170-1563-45de-ba70-6f978df33eb2",
  "date_created": "2026-03-02T18:01:52.225000Z",
  "date_modified": "2026-03-02T18:01:52.225000Z",
  "file_hash": "381f16eb52b47e396bfa18ba78c4ffba39ef97021ce603b803fa4aeda6382ca5",
  "private": false,
  "record": {
    "abstract": "There exist a number of typical and interesting systems or models which\npossess three-generator Lie-algebraic structure in atomic physics, quantum\noptics, nuclear physics and laser physics. The well-known fact that all simple\n3-generator algebras are either isomorphic to the algebra $sl(2,C)$ or to one\nof its real forms enables us to treat these time-dependent quantum systems in a\nunified way. By making use of the Lewis-Riesenfeld invariant theory and the\ninvariant-related unitary transformation formulation, the present paper obtains\nexact solutions of the time-dependent Schr\\\"{o}dinger equations governing\nvarious three-generator quantum systems. For some quantum systems whose\ntime-dependent Hamiltonians have no quasialgebraic structures, we show that the\nexact solutions can also be obtained by working in a sub-Hilbert-space\ncorresponding to a particular eigenvalue of the conserved generator (i.e., the\ntime-independent invariant that commutes with the time-dependent Hamiltonian).\nThe topological property of geometric phase factors in time-dependent systems\nis briefly discussed.",
    "arxiv_id": "quant-ph/0205170",
    "authors": [
      "Jian-Qi Shen",
      "Hong-Yi Zhu",
      "Pan Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Exact solutions of time-dependent three-generator systems",
    "url": "https://arxiv.org/abs/quant-ph/0205170"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8c4ef544-7c23-4d29-b874-a3bf41d1c307",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}