{
  "annotation_id": "66f1dc48-51d9-4133-ad0f-726b57d75821",
  "date_created": "2026-03-02T18:01:58.923000Z",
  "date_modified": "2026-03-02T18:01:58.923000Z",
  "file_hash": "70e9a4ee5cdc4ae380b55ce952cfeb946e42f0e2acb5506dcc1f6c4e64875e54",
  "private": false,
  "record": {
    "abstract": "Central D-dimensional Hamiltonians $H = p^2 + a |\\vec{r}|^2 + b |\\vec{r}|^4 +\n\u003e... + z |\\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \\to\n\\infty$ where numerical experiments revealed recently a new class of\nq-parametric quasi-exact solutions at $q \\leq 5$. We show how a systematic\nconstruction of these \"privileged\" exact bound states may be extended to much\nhigher q (meaning an enhanced flexibility of the shape of the force) at a cost\nof narrowing the set of wavefunctions (with degree N restricted to the first\nfew non-negative integers). At q=4K+3 we conjecture the validity of a closed\nformula for the N=3 solutions at all K.",
    "arxiv_id": "quant-ph/0304170",
    "authors": [
      "Miloslav Znojil"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Rendiconti del Circolo Matematico di Palermo, Ser. II, Suppl. 75\n  (2005) 333-346.",
    "title": "Multiparametric oscillator Hamiltonians with exact bound states in   infinite-dimensional space",
    "url": "https://arxiv.org/abs/quant-ph/0304170"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c4f69c3c-083a-475b-8c6a-37593467d40e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}