{"id":"W1547485441","doi":"10.1088/0253-6102/55/5/10","title":"New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators","year":2011,"lang":"en","type":"article","venue":"Communications in Theoretical Physics","topic":"Cold Atom Physics and Bose-Einstein Condensates","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Ontario Centres of Excellence","keywords":"Operator (biology); Realization (probability); Exponential function; Physics; Angular momentum; Angular momentum operator; Momentum (technical analysis); Decomposition; Lie algebra; Operator theory; Mathematical physics; Pure mathematics; Algebra over a field; Mathematics; Total angular momentum quantum number; Quantum mechanics; Mathematical analysis; Angular momentum coupling; Statistics; Chemistry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001540823,0.0001837675,0.0003118002,0.00004020445,0.00013469,0.00003289646,0.0008347137,0.00003721778,0.0002638765],"category_scores_gemma":[0.000009293561,0.0001765435,0.0001748124,0.0002340116,0.0005885996,0.0001170884,0.0003706843,0.0001723632,0.000009521332],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002923351,"about_ca_system_score_gemma":0.00007789084,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000908685,"about_ca_topic_score_gemma":0.000003058444,"domain_scores_codex":[0.9988905,0.0000905383,0.0004201199,0.0002222301,0.0001292802,0.000247288],"domain_scores_gemma":[0.9983568,0.0002027612,0.0001141947,0.001098193,0.0001227554,0.0001053213],"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":[0.00003357058,0.000570552,0.003773076,0.00001098168,0.00006193523,1.67421e-7,0.001079368,0.00001473176,0.00531049,0.9825341,0.00005994475,0.006551043],"study_design_scores_gemma":[0.001842605,0.0001391664,0.0002787173,0.0001062256,0.0000940212,1.375487e-7,0.001478917,0.01416189,0.1812335,0.7997258,0.0005377821,0.0004012585],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8856097,0.0002836615,0.09562043,0.0004116993,0.0003665049,0.001509176,0.0002382353,0.00005978701,0.01590084],"genre_scores_gemma":[0.9908309,0.000007662687,0.008743187,0.00002548944,0.0001416315,0.00008677194,0.0001096155,0.00002941378,0.0000253283],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1828083,"threshold_uncertainty_score":0.7199237,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03716725625541638,"score_gpt":0.2844638374836999,"score_spread":0.2472965812282835,"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."}}