{"paper":{"title":"Quantum Tunneling and Caustics under Inverse Square Potential","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Hitoshi Miyazaki, Izumi Tsutsui","submitted_at":"2002-02-06T13:08:17Z","abstract_excerpt":"Quantization of a harmonic oscillator with inverse square potential $V(x)=(m{\\omega^2}/2){x^2}+g/{x^2}$ on the line $-\\infty<x<\\infty$ is re-examined. It is shown that, for $0<g<3{\\hbar^2}/(8m)$, the system admits a U(2) family of inequivalent quantizations allowing for quantum tunneling through the potenatial barrier at $x=0$. In the family is a distinguished quantization which reduces smoothly to the harmonic oscillator as $g\\to 0$, in contrast to the conventional quantization applied to the Calogero model which prohibits the tunneling and has no such limit. The tunneling renders the classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0202037","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}