The Scattering amplitude for one parameter family of shape invariant potentials related to Xm Jacobi polynomials

Abstract

We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized Pöschl-Teller potential. By explicitly considering the asymptotic behaviour of the Xm Jacobi polynomials associated with this system (m = 1, 2, 3, ...), the scattering amplitude for the one parameter family of potentials is calculated explicitly.

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References in corpus (4)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Exceptional orthogonal polynomials and the Darboux transformation
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials

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• The Scattering amplitude for Rationally extended shape invariant Eckart potentials
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• Scattering Amplitudes for Multi-indexed Extensions of Solvable Potentials
• A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
• A proof of the Veselov Conjecture for segments