{"id":"W21687839","doi":"10.1039/c1em10088b","title":"Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator","year":2004,"lang":"en","type":"article","venue":"理论物理通讯：英文版","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Dirac (video compression format); Dirac algebra; Matrix (chemical analysis); Dirac equation; Square (algebra); Dirac operator; Operator (biology); Mathematics; Physics; Quantum mechanics; Mathematical physics; Geometry; Chemistry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002419495,0.0001588892,0.0005985684,0.000250613,0.00006938261,0.00000902083,0.0002183919,0.00008227299,0.000113853],"category_scores_gemma":[0.0007189436,0.0001257897,0.0003986242,0.0005853607,0.0001413225,0.00008372367,0.00008214171,0.00008153363,0.00001556739],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000389199,"about_ca_system_score_gemma":0.00007451705,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006791036,"about_ca_topic_score_gemma":0.00001272647,"domain_scores_codex":[0.9985095,0.00002366092,0.0005571159,0.0002138597,0.0004353112,0.0002605272],"domain_scores_gemma":[0.9984841,0.0005725272,0.0003019061,0.0003714866,0.0001785778,0.00009134256],"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":[0.0001311405,0.001446468,0.003474942,0.0006220829,0.0007900783,0.000003354991,0.003258108,0.0002262075,0.001872044,0.9820306,0.005399805,0.0007451196],"study_design_scores_gemma":[0.00797599,0.001910283,0.002893942,0.0007221337,0.003579136,0.000006143046,0.01750922,0.01076124,0.08786213,0.8560727,0.009290838,0.001416239],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9568349,0.0001125279,0.04102997,0.0001248638,0.00004952777,0.0002644841,0.0001295556,0.00003444204,0.0014198],"genre_scores_gemma":[0.9871237,0.00001308501,0.01132322,0.00002110745,0.00009741576,0.00001791048,0.00001153517,0.00002146322,0.00137057],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1259579,"threshold_uncertainty_score":0.5129556,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05113897518159779,"score_gpt":0.3782686664926008,"score_spread":0.3271296913110031,"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."}}