{"id":"W2993852729","doi":"10.3390/quantum1020027","title":"Hamilton Equations, Commutator, and Energy Conservation","year":2019,"lang":"en","type":"article","venue":"Quantum Reports","topic":"Quantum Electrodynamics and Casimir Effect","field":"Physics and Astronomy","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Hong Kong Government; McGill University; Purdue University; National Science Foundation","keywords":"Equations of motion; Hamiltonian (control theory); Method of quantum characteristics; Quantum; Commutator; Heisenberg picture; Mathematical physics; Classical mechanics; Physics; Mathematics; Quantum dynamics; Quantum mechanics; Quantum operation","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007694081,0.0003490936,0.0003741819,0.0005536875,0.000884874,0.000960611,0.0007001881,0.0008748898,0.01296247],"category_scores_gemma":[0.001091496,0.0001851241,0.0004344636,0.0004760961,0.002046175,0.002276161,0.001153191,0.001325839,0.001375777],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001110357,"about_ca_system_score_gemma":0.001202145,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004759237,"about_ca_topic_score_gemma":0.004430489,"domain_scores_codex":[0.9995317,0.00009576103,0.00003357348,0.00009034684,0.0001805463,0.00006807027],"domain_scores_gemma":[0.9996616,0.0000977379,0.00004836301,0.00004604004,0.0001173226,0.00002890067],"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":[0.00000125546,0.000003108488,0.00003196598,0.00001058924,0.000001153181,0.000025546,0.00006582787,0.0001790118,0.0001725907,0.996498,0.001454553,0.001556347],"study_design_scores_gemma":[0.000007743971,0.00000810262,0.0001612731,0.00001092361,0.000002126031,0.00008888703,0.00003098395,0.002647957,0.0001665988,0.9792628,0.01760467,0.00000801542],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04774088,0.006758926,0.2799617,0.01120631,0.001487833,0.0002383777,0.001179314,0.0002022242,0.6512244],"genre_scores_gemma":[0.6923642,0.007141486,0.1201394,0.003786911,0.001509039,0.0005437546,0.001016591,0.0002082073,0.1732904],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01296247,"threshold_uncertainty_score":0.04336375,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004313376232772251,"score_gpt":0.2151194477009102,"score_spread":0.210806071468138,"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."}}