{
  "annotation_id": "139107bb-cd31-4faa-a07b-7a7e41ef18ed",
  "date_created": "2026-03-02T18:02:44.980000Z",
  "date_modified": "2026-03-02T18:02:44.980000Z",
  "file_hash": "aba04f79a81614cd68237f93aa33e814f31249a4fcd59f45db2eca0d901910f7",
  "private": false,
  "record": {
    "abstract": "The Schr\\\"{o}dinger equation with the central potential is first studied in\nthe arbitrary dimensional spaces and obtained an analogy of the two-dimensional\nSchr\\\"{o}dinger equation for the radial wave function through a simple\ntransformation. As an example, applying an ${\\it ansatz}$ to the\neigenfunctions, we then arrive at an exact closed form solution to the modified\ntwo-dimensional Schr\\\"{o}dinger equation with the octic potential,\n$V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.",
    "arxiv_id": "quant-ph/9901037",
    "authors": [
      "Shi-Hai Dong",
      "Zhong-Qi Ma"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Exact Solution to the Schr\\\"{o}dinger Equation with the Octic   Potential",
    "url": "https://arxiv.org/abs/quant-ph/9901037"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ebc30cf2-3a10-4268-a05c-249461d02152",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}