{
  "annotation_id": "b37259b9-e604-4fcb-9c8e-b3e8f77858b1",
  "date_created": "2026-03-02T18:02:27.047000Z",
  "date_modified": "2026-03-02T18:02:27.047000Z",
  "file_hash": "ac1c943c0a4d7723949a66f5af858c2a813681e8ab7137c145a05e7ada32c3eb",
  "private": false,
  "record": {
    "abstract": "We discuss exact solutions of the Schroedinger equation for the system of two\nultracold atoms confined in an axially symmetric harmonic potential. We\ninvestigate different geometries of the trapping potential, in particular we\nstudy the properties of eigenenergies and eigenfunctions for quasi-one- and\nquasi-two-dimensional traps. We show that the quasi-one- and the\nquasi-two-dimensional regimes for two atoms can be already realized in the\ntraps with moderately large (or small) ratios of the trapping frequencies in\nthe axial and the transverse directions. Finally, we apply our theory to\nFeshbach resonances for trapped atoms. Introducing in our description an\nenergy-dependent scattering length we calculate analytically the eigenenergies\nfor two trapped atoms in the presence of a Feshbach resonance.",
    "arxiv_id": "quant-ph/0604205",
    "authors": [
      "Zbigniew Idziaszek",
      "Tommaso Calarco"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.022712",
    "journal_ref": "Phys. Rev. A 74, 022712 (2006)",
    "title": "Analytical solutions for the dynamics of two trapped interacting   ultracold atoms",
    "url": "https://arxiv.org/abs/quant-ph/0604205"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1886bd87-184f-45d9-a581-0130b015b17d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}