{"paper":{"title":"Quasiclassical Asymptotics and Coherent States for Bounded Discrete Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. Horzela, A. I. Solomon, G. H. E. Duchamp, K. A. Penson, K. Gorska, P. Blasiak","submitted_at":"2010-07-15T16:55:49Z","abstract_excerpt":"We consider discrete spectra of bound states for non-relativistic motion in attractive potentials V_{\\sigma}(x) = -|V_{0}| |x|^{-\\sigma}, 0 < \\sigma \\leq 2. For these potentials the quasiclassical approximation for n -> \\infty predicts quantized energy levels e_{\\sigma}(n) of a bounded spectrum varying as e_{\\sigma}(n) ~ -n^{-2\\sigma/(2-\\sigma)}. We construct collective quantum states using the set of wavefunctions of the discrete spectrum taking into account this asymptotic behaviour. We give examples of states that are normalizable and satisfy the resolution of unity, using explicit positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2617","kind":"arxiv","version":2},"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"}