The Scattering amplitude for Rationally extended shape invariant Eckart potentials

Abstract

We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally ex- tended potentials is calculated analytically for the generalized mth (m = 1, 2, 3, ...) case by considering the asymptotic behavior of the scattering state wave functions which are written in terms of some new polynomials related to the Jacobi polyno- mials. As expected, in the m = 0 limit, this scattering amplitude goes over to the scattering amplitude for the conventional Eckart potential.

8 pages. Latex, No fig

References in corpus (6)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Exceptional orthogonal polynomials and the Darboux transformation
• Extensions of solvable potentials with finitely many discrete eigenstates
• The Scattering amplitude for Newly found exactly solvable Potential
• The Scattering amplitude for one parameter family of shape invariant potentials related to Xm Jacobi polynomials

Cited by in corpus (10)

• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• A Bochner type classification theorem for exceptional orthogonal polynomials
• Group theoretic approach to rationally extended shape invariant potentials
• Quantum mechanics with orthogonal polynomials
• Orthogonal polynomials derived from the tridiagonal representation approach
• 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
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra