{
  "annotation_id": "e5a73c74-ff6e-4a77-a108-25f713eb82a9",
  "date_created": "2026-03-02T18:02:38.097000Z",
  "date_modified": "2026-03-02T18:02:38.097000Z",
  "file_hash": "414a52162b2307c133859d25609560002d4775c35d7a55eb1ab1767c0c99c544",
  "private": false,
  "record": {
    "abstract": "Time-dependent unitary transformations are used to study the Schreodinger\nequation for explicitly time-dependent Hamiltonians of the form $H(t)=\\vec\nR(t).\\vec J$, where $\\vec R$ is an arbitrary real vector-valued function of\ntime and $\\vec J$ is the angular momentum operator. The solution of the\nSchreodinger equation for the most general Hamiltonian of this form is shown to\nbe equivalent to the special case $\\vec R=(1,0,\\nu(t))$. This corresponds to\nthe problem of driven two-level atom for the spin half representation of $\\vec\nJ$. It is also shown that by requiring the magnitude of $\\vec R$ to depend on\nits direction in a particular way, one can solve the Schreodinger equation\nexactly. In particular, it is shown that for every Hamiltonian of the form\n$H(t)=\\vec R(t)\\cdot \\vec J$ there is another Hamiltonian with the same\neigenstates for which the Schreodinger equation is exactly solved. The\napplication of the results to the exact solution of the parallel transport\nequation and exact holonomy calculation for SU(2) principal bundles (Yang-Mills\ngauge theory) is also pointed out.",
    "arxiv_id": "quant-ph/9611052",
    "authors": [
      "Ali Mostafazadeh"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1063/1.531864",
    "journal_ref": "J.Math.Phys. 38 (1997) 3489-3496",
    "title": "Quantum Canonical Transformations and Exact Solution of the Schreodinger   Equation",
    "url": "https://arxiv.org/abs/quant-ph/9611052"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "38cd2c44-ffbd-44d5-852c-30543d92eabc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}