{
  "annotation_id": "ee3a565c-1cc8-4877-96ce-a173c5550b59",
  "date_created": "2026-03-02T18:02:45.178000Z",
  "date_modified": "2026-03-02T18:02:45.178000Z",
  "file_hash": "4dab7a94405fb59b04120238b840bd57864697a899b3c3d7dda64e833c0eee47",
  "private": false,
  "record": {
    "abstract": "Borel summable semiclassical expansions in 1D quantum mechanics are\nconsidered. These are the Borel summable expansions of fundamental solutions\nand of quantities constructed with their help. An expansion, called\ntopological,is constructed for the corresponding Borel functions. Its main\nproperty is to order the singularity structure of the Borel plane in a\nhierarchical way by an increasing complexity of this structure starting from\nthe analytic one. This allows us to study the Borel plane singularity structure\nin a systematic way. Examples of such structures are considered for linear,\nharmonic and anharmonic potentials. Together with the best approximation\nprovided by the semiclassical series the exponentially small contribution\ncompleting the approximation are considered. A natural method of constructing\nsuch an exponential asymptotics relied on the Borel plane singularity\nstructures provided by the topological expansion is developed. The method is\nused to form the semiclassical series including exponential contributions for\nthe energy levels of the anharmonic oscillator.",
    "arxiv_id": "quant-ph/9903097",
    "authors": [
      "Stefan Giller"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/33/8/304",
    "journal_ref": "J.Phys.A33:1543-1580,2000",
    "title": "Topological Expansion and Exponential Asymptotics in 1D Quantum   Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9903097"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cafd5f26-b05d-4474-96f7-763efa48624c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}