{"paper":{"title":"Contribution to understanding the mathematical structure of quantum mechanics","arxiv_id":"quant-ph/0602182","primary_cat":"quant-ph","submitted_at":"2006-02-22T13:52:58+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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probabilistic description of results of measurement of the space coordinates and time.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.86,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.85,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.15,"interpretation":0.0}},{"i":2,"p":0.85,"id":"s2","own":true,"role":"result","text":"Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.85,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.11,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"result","text":"The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.77,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.02}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"contribution","text":"Many particle systems and the postulates of quantum mechanics are also discussed.","hedge":{"p":0.63,"label":"asserted"},"own_p":0.57,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, 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