{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002402301,0.0001360454,0.0001840207,0.00005033636,0.00009492561,0.00006026804,0.00004386389,0.00003763725,0.0001707469],"category_scores_gemma":[0.000006688523,0.000130704,0.00005725312,0.0001094393,0.00003023159,0.0001216652,0.00002390639,0.00009290034,0.00001691836],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001798454,"about_ca_system_score_gemma":0.00005383556,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008087118,"about_ca_topic_score_gemma":0.00001555184,"domain_scores_codex":[0.9990609,0.00005361665,0.0002782138,0.0002580112,0.0001469068,0.0002022971],"domain_scores_gemma":[0.9992423,0.0001196888,0.0001956901,0.0003249934,0.00005587278,0.00006144759],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001490711,0.00009660157,0.1913534,0.00002100414,0.00007174328,0.00002792729,0.0001478748,0.00005705515,0.005970514,0.7918714,0.001180039,0.009187547],"study_design_scores_gemma":[0.001279613,0.0006277631,0.03639672,0.000131147,0.0001007628,0.0001630125,0.0004198458,0.470298,0.003957272,0.3575371,0.1278391,0.001249698],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9842528,0.0001439361,0.009111522,0.0001753322,0.0002827015,0.0001076962,0.000004835143,0.0000398491,0.005881398],"genre_scores_gemma":[0.9989162,0.000007920763,0.00004068707,0.0001538404,0.00006112749,0.00002350294,0.0001340877,0.00001970146,0.000642909],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.470241,"threshold_uncertainty_score":0.5329956,"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."}}