{"id":"W2027215338","doi":"10.1063/1.3567438","title":"Hilbert Space of the Bicomplex Quantum Harmonic Oscillator","year":2011,"lang":"en","type":"article","venue":"AIP conference proceedings","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Trois-Rivières","funders":"Natural Sciences and Engineering Research Council of Canada; Fonds Québécois de la Recherche sur la Nature et les Technologies","keywords":"Harmonic oscillator; Eigenfunction; Hilbert space; Hamiltonian (control theory); Hermite polynomials; Eigenvalues and eigenvectors; Quantum harmonic oscillator; Basis (linear algebra); Mathematics; Physics; Pure mathematics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003182002,0.0001951043,0.0003663886,0.0001543718,0.0001209551,0.00002808507,0.0006143995,0.0001029454,0.0009135024],"category_scores_gemma":[0.0006621126,0.000127448,0.0001843941,0.0009909671,0.000224851,0.000155362,0.0002014286,0.0001908375,0.00005363188],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003582726,"about_ca_system_score_gemma":0.0001007435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001691879,"about_ca_topic_score_gemma":0.000008508508,"domain_scores_codex":[0.9986395,0.00001130094,0.0003682129,0.0002833948,0.0003906796,0.0003069002],"domain_scores_gemma":[0.9987092,0.00009646713,0.000378973,0.0002604742,0.0004651631,0.00008974334],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001840994,0.0001184264,0.07320031,0.0001111083,0.000133783,4.861773e-7,0.004864886,7.78014e-9,0.002446329,0.913048,0.005673424,0.0003848441],"study_design_scores_gemma":[0.000662811,0.000223456,0.06184413,0.000206358,0.0005376587,0.00001692637,0.004959825,0.003550846,0.01424953,0.9085595,0.004536301,0.0006526263],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9594735,0.0001012291,0.006879951,0.0007716413,0.000111464,0.0002743482,0.000005431074,0.00009208275,0.03229038],"genre_scores_gemma":[0.9955053,0.00002990189,0.002283683,0.00007558265,0.00003453292,0.00001321265,3.370764e-7,0.00002010526,0.002037341],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03603183,"threshold_uncertainty_score":0.9999998,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0923261171165877,"score_gpt":0.2745443960168362,"score_spread":0.1822182789002485,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}