{"paper":{"title":"Landau-Lifshitz's conjecture about the motion of a quantum mechanical particle under the inverse square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Motohiro Sobajima, Shuji Watanabe","submitted_at":"2013-12-10T12:21:21Z","abstract_excerpt":"Landau and Lifshitz [4, Section 35] conjectured that for an arbitrary $k\\in \\mathbb{R}$, there exists the motion of a quantum mechanical particle under the inverse square potential $k|x|^{-2}$, $x \\in \\mathbb{R}^3$. When $k$ is negative and $| k |$ is very large, the inverse square potential becomes very deep and generates the very strong attractive force, and hence a quantum mechanical particle is likely to fall down to the origin (the center of the inverse square potential). Therefore this conjecture (Landau-Lifshitz's conjecture) seems to be wrong at first sight. We however prove Landau-Lif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2774","kind":"arxiv","version":1},"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"}