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The Real Exact Solutions to the Hyperbolic Scarf Potential

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arxiv quant-ph/0603122 v4 pith:FDUCGVSZ submitted 2006-03-14 quant-ph

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keywords solutionsequationexacthyperbolicpolynomialspotentialrealscarf
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The exact solutions of the Schrodinger equation with the hyperbolic Scarf potential reported in the literature so far rely upon Jacobi polynomials with imaginary arguments and parameters. We here show that upon a suitable factorization these solutions can be expressed alternatively by means of real orthogonal polynomials distinct but the classical ones as they satisfy a new self-adjoint differential equation of the hypergeometric type.

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Cited by 1 Pith paper

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  1. Flyby-induced displacement: analytic solution

    gr-qc 2025-02 accept novelty 5.0 of 10

    The authors derive exact analytic solutions for gravitational wave displacement memory when the flyby profile is approximated by the hyperbolic Scarf potential, with magic amplitude values |g|=(2n+1) sqrt(n(n+1)).

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