{"id":"W4386472827","doi":"10.1109/tmtt.2023.3308198","title":"Calculation and Conservation of Probability and Energy in the Numerical Solution of the Schrödinger Equation With the Finite- Difference Time-Domain Method","year":2023,"lang":"en","type":"article","venue":"IEEE Transactions on Microwave Theory and Techniques","topic":"Electromagnetic Simulation and Numerical Methods","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"University of Toronto; Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Finite difference method; Schrödinger equation; Conservation of energy; Energy conservation; Mathematical analysis; Mathematics; Finite difference; Applied mathematics; Finite-difference time-domain method; Energy (signal processing); Time domain; Conservation law; Physics; Computer science; Quantum mechanics; Engineering; Statistics; Electrical engineering","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001249917,0.0002494993,0.0003876721,0.0004872911,0.0005082851,0.0008414601,0.0008567778,0.0008178132,0.001393018],"category_scores_gemma":[0.003598221,0.0002161416,0.0004479168,0.0004117808,0.001181995,0.001258359,0.0006715117,0.0007953589,0.0002732953],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005659479,"about_ca_system_score_gemma":0.001139714,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001349941,"about_ca_topic_score_gemma":0.0008715637,"domain_scores_codex":[0.9995856,0.00009928201,0.00002609564,0.00003249533,0.0002314511,0.00002510661],"domain_scores_gemma":[0.9990772,0.0004976569,0.00006365181,0.0001238548,0.0002129676,0.00002476911],"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":[0.00004311365,0.00005958473,0.0007299462,0.0001889003,0.0000187589,0.0002219056,0.0003195398,0.2733986,0.02467403,0.6652588,0.001225759,0.03386118],"study_design_scores_gemma":[0.00001006032,0.00001105364,0.00008278069,0.00001216603,0.000003059903,0.00006808678,0.00001434627,0.9668304,0.003299081,0.02779366,0.00186687,0.000008512744],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008040584,0.00008034122,0.9882442,0.0001331541,0.00003877519,0.00003465538,0.00001635313,0.00005997896,0.003351847],"genre_scores_gemma":[0.2649266,0.0003429345,0.7296891,0.0001349775,0.00003973983,0.0002314356,0.00006684261,0.00009327008,0.004475174],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001393018,"threshold_uncertainty_score":0.006610215,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01679519413596607,"score_gpt":0.2568384901570113,"score_spread":0.2400432960210452,"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."}}