{"paper":{"title":"Finite dimensional quantizations of the (q,p) plane : new space and momentum inequalities","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Fran\\c{c}ois-Xavier Josse-Michaux (APC), Jean-Pierre Gazeau (APC), Pascal Monceau (MSC)","submitted_at":"2004-11-30T14:51:30Z","abstract_excerpt":"We present a N-dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of position and momentum operators are finite and eigenvalues are equal, up to a factor, to the zeros of Hermite polynomials. From numerical and theoretical studies of the large $N$ behavior of the product $\\lambda\\_m(N) \\lambda\\_M(N)$ of non null smallest positive and largest eigenvalues, we infer the inequality $\\delta\\_N(Q) \\Delta\\_N(Q) = \\sigma\\_N \\overset{<}{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0411210","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"}