{"paper":{"title":"Inequivalent quantizations of the three-particle Calogero model constructed by separation of variables","license":"","headline":"","cross_cats":["hep-th","math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"I. Tsutsui, L. Feher, T. Fulop","submitted_at":"2004-12-30T13:17:01Z","abstract_excerpt":"We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\\\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the angular and radial Hamiltonians. The inverse square coupling constant is taken to be $g=2\\nu (\\nu-1)$ with ${1/2} <\\nu< {3/2}$ and then the angular Hamiltonian is shown to admit a 2-parameter family of inequivalent quantizations compatible with the dihedral $D_6$ symmetry of its potential term $9 \\nu (\\nu -1)/\\sin^2 3\\phi$. These are parametrized by a matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0412095","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0412095/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}