{"paper":{"title":"Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation","arxiv_id":"quant-ph/0603023","primary_cat":"quant-ph","submitted_at":"2006-03-03T09:58:39+00:00","version_compiled":"v2"},"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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term.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.16,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.77,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.04}},{"i":2,"p":0.73,"id":"s2","own":true,"role":"result","text":"We obtain a general series solution of this equation that involves a pair of arbitrary functions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.47,"role_probabilities":{"gap":0.0,"method":0.08,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.19,"interpretation":0.0}},{"i":3,"p":0.94,"id":"s3","own":true,"role":"interpretation","text":"These characterize the arbitrariness in the choice of \\eta.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.72,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.06,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.94}},{"i":4,"p":0.74,"id":"s4","own":true,"role":"contribution","text":"We apply our general results to calculate \\eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.23,"result":0.03,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.74,"interpretation":0.0}},{"i":5,"p":0.75,"id":"s5","own":true,"role":"result","text":"For the first two systems, our method reproduces the known results in a straightforward and extremely efficient 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