{
  "annotation_id": "fee8d370-9173-4120-aa60-0562b4d34ae5",
  "date_created": "2026-03-02T18:02:41.594000Z",
  "date_modified": "2026-03-02T18:02:41.594000Z",
  "file_hash": "9cb684b3526ca80131f1775347a0deb85856a7738cf857981ce0b2f6d7e3d62d",
  "private": false,
  "record": {
    "abstract": "It is shown that so called fundamental solutions the semiclassical expansions\nof which have been established earlier to be Borel summable to the solutions\nthemselves appear also to be the unique solutions to the 1D Schr\\\"odinger\nequation having this property. Namely, it is shown in this paper that for the\npolynomial potentials the Borel function defined by the fundamental solutions\ncan be considered as the canonical one. The latter means that any Borel\nsummable solution can be obtained by the Borel transformation of this unique\ncanonical Borel function multiplied by some $\\hbar$-dependent and Borel\nsummable constant. This justify the exceptional role the fundamental solutions\nplay in 1D quantum mechanics and completes the relevant semiclassical theory\nrelied on the Borel resummation technique and developed in our other papers.",
    "arxiv_id": "quant-ph/9801031",
    "authors": [
      "Stefan Giller",
      "Piotr Milczarski"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1331099",
    "journal_ref": "J.Math.Phys. 42 (2001) 608-640",
    "title": "Borel Summable Solutions to 1D Schr\\\"odinger Equation",
    "url": "https://arxiv.org/abs/quant-ph/9801031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4a0dbdf7-62fc-4d7a-904b-d4afe4a88406",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}