{
  "annotation_id": "33db7b00-f684-475e-8c2c-058a7ded2981",
  "date_created": "2026-03-02T18:01:56.064000Z",
  "date_modified": "2026-03-02T18:01:56.064000Z",
  "file_hash": "fd4b8914edc30a0f8484e3ed46c8065a70f33d01e028ae9157f960ff8d4c157f",
  "private": false,
  "record": {
    "abstract": "We study the radial Schroedinger equation for a particle in the field of a\nsingular inverse square attractive potential. This potential is relevant to the\nfabrication of nanoscale atom optical devices, is said to be the potential\ndescribing the dipole-bound anions of polar molecules, and is the effective\npotential underlying the universal behavior of three-body systems in nuclear\nphysics and atomic physics, including aspects of Bose-Einstein condensates,\nfirst described by Efimov. New results in three-body physical systems motivate\nthe present investigation. Using the regularization method of Beane et al., we\nshow that the corresponding ``renormalization group flow\u0027\u0027 equation can be\nsolved analytically. We find that it exhibits a limit cycle behavior and has\ninfinitely many branches. We show that a physical meaning for self-adjoint\nextensions of the Hamiltonian arises naturally in this framework.",
    "arxiv_id": "quant-ph/0302199",
    "authors": [
      "M. Bawin",
      "S. A. Coon"
    ],
    "categories": [
      "quant-ph",
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevA.67.042712",
    "journal_ref": "Phys.Rev.A67:042712,2003",
    "title": "The singular inverse square potential, limit cycles and self-adjoint   extensions",
    "url": "https://arxiv.org/abs/quant-ph/0302199"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d9c11134-7715-48fb-9c62-a53fd6c11b9e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}