{"id":"W2754635203","doi":"10.48550/arxiv.1709.04759","title":"The hydrogen atom according to wave mechanics in cartesian coordinates","year":2017,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Cartesian coordinate system; Polar coordinate system; Angular momentum; Hydrogen atom; Algebraic number; Separation of variables; Quantum number; Schrödinger equation; Physics; Atom (system on chip); Quantum; Spherical coordinate system; Variable (mathematics); Wave function; Generalized coordinates; Momentum (technical analysis); Total angular momentum quantum number; Quantum mechanics; Mathematics; Log-polar coordinates; Mathematical analysis; Geometry; Partial differential equation","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003649766,0.0003827689,0.0002528223,0.0004353433,0.0006743473,0.001616335,0.0006512565,0.0007081692,0.01144522],"category_scores_gemma":[0.0006501489,0.0001842485,0.0002383087,0.000555955,0.001140281,0.001607207,0.0007057455,0.0007667384,0.002261036],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003651318,"about_ca_system_score_gemma":0.0007144719,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002155121,"about_ca_topic_score_gemma":0.001420254,"domain_scores_codex":[0.9997427,0.00007819727,0.000008533209,0.00002971384,0.0001073525,0.00003347703],"domain_scores_gemma":[0.9998549,0.00002335343,0.00001408452,0.00003737723,0.00005575112,0.00001450759],"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":[0.00001451986,0.000009004464,0.0001945754,0.00002730969,0.000005381921,0.00005321171,0.0001418289,0.003347136,0.002256959,0.9837065,0.003131604,0.007111908],"study_design_scores_gemma":[0.00007345816,0.00009087583,0.001612887,0.00003908103,0.000009947047,0.0002829601,0.0004419974,0.08637307,0.002919449,0.8528435,0.05527762,0.00003518824],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1861876,0.001492133,0.4858218,0.003256745,0.001240694,0.0003890647,0.0009815366,0.0007036639,0.3199268],"genre_scores_gemma":[0.7461535,0.001927259,0.1511476,0.0008477984,0.0002598708,0.0003148218,0.0007597204,0.000367614,0.09822173],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01144522,"threshold_uncertainty_score":0.03828812,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04941188858390614,"score_gpt":0.2036537798171832,"score_spread":0.1542418912332771,"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."}}