{
  "annotation_id": "7189ac4a-8de1-48cb-904e-04eea466646a",
  "date_created": "2026-03-02T18:02:47.594000Z",
  "date_modified": "2026-03-02T18:02:47.594000Z",
  "file_hash": "844d37bbbfcbb38dc5d53f68d2f4077cfad9b196a6411a89b09b76f8215557f1",
  "private": false,
  "record": {
    "abstract": "The three-dimensional Schredinger\u0027s equation is analyzed with the help of the\ncorrespondence principle between classical and quantum-mechanical quantities.\nSeparation is performed after reduction of the original equation to the form of\nthe classical Hamilton-Jacobi equation. Each one-dimensional equation obtained\nafter separation is solved by the conventional WKB method. Quasiclassical\nsolution of the angular equation results in the integral of motion $\\vec\nM^2=(l+\\frac 12)^2\\hbar^2$ and the existence of nontrivial solution for the\nangular quantum number $l=0$. Generalization of the WKB method for\nmulti-turning-point problems is given. Exact eigenvalues for solvable and some\n\"insoluble\" spherically symmetric potentials are obtained. Quasiclassical\neigenfunctions are written in terms of elementary functions in the form of a\nstanding wave.",
    "arxiv_id": "quant-ph/9912069",
    "authors": [
      "M. N. Sergeenko"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217732300000104",
    "journal_ref": "Mod. Phys. Lett. A, 15(2) (2000) 83",
    "title": "Quasiclassical Analysis of the Three-dimensional Shredinger\u0027s Equation   and its Solution",
    "url": "https://arxiv.org/abs/quant-ph/9912069"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b3caa3e8-4e15-44a0-aa28-9a6ebbc8c873",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}