{"paper":{"title":"Riemann Hypothesis, Modified Morse Potential and Supersymmetric Quantum Mechanics","arxiv_id":"2002.12825","primary_cat":"math-ph","submitted_at":"2020-02-28T15:54:19+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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potential.","hedge":{"p":0.62,"label":"asserted"},"own_p":0.37,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.01,"background":0.31,"limitation":0.0,"future_work":0.0,"contribution":0.64,"interpretation":0.0}},{"i":2,"p":0.95,"id":"s2","own":true,"role":"method","text":"We use supersymmetric quantum mechanics to construct their ground state wave functions and the Fourier transform of the ground state to exhibit the Riemann zeros.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.95,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":3,"p":0.65,"id":"s3","own":true,"role":"interpretation","text":"This allows us to formulate the Riemann hypothesis in terms of the location of the nodes of the ground state wave function in momentum space.","hedge":{"p":0.87,"label":"asserted"},"own_p":0.85,"main_claim_p":0.42,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.18,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.15,"interpretation":0.65}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"contribution","text":"We also discuss the relation these potentials to one and two matrix integrals and construct a few orthogonal polynomials associated with the matrix models.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.44,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.99,"interpretation":0.0}},{"i":5,"p":0.52,"id":"s5","own":true,"role":"method","text":"We relate the Schrodinger equation in momentum space to and finite difference equation in momentum space with an infinite number of terms.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.87,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.0,"method":0.52,"result":0.06,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.42,"interpretation":0.0}},{"i":6,"p":0.52,"id":"s6","own":true,"role":"result","text":"We computed the uncertainty relations associated with these potentials and ground states as well as the Shannon Information entropy and compare with the unmodified Morse and harmonic oscillator potentials.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.6,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.52,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.44,"interpretation":0.0}},{"i":7,"p":0.9,"id":"s7","own":true,"role":"future_work","text":"Finally we discuss the extension of these methods to other functions defined by a Dirichlet series such as the the Ramanujan 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