The Scattering amplitude for Newly found exactly solvable Potential

Abstract

The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized Pöschl-Taylor potential, is calculated explicitly by considering the asymptotic behavior of the $X_1$ Jacobi exceptional polynomials associated with this system.

arXiv comment6 pages, Latex

References in corpus (7)

• Supersymmetry and Quantum Mechanics
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
• Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
• Exceptional orthogonal polynomials and the Darboux transformation

Cited by in corpus (14)

• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• The Scattering amplitude for one parameter family of shape invariant potentials related to Xm Jacobi polynomials
• The Scattering amplitude for Rationally extended shape invariant Eckart potentials
• Group theoretic approach to rationally extended shape invariant potentials
• 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
• Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Rationally extended many-body truncated Calogero-Sutherland model
• Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
• Scattering Amplitudes for Multi-indexed Extensions of Soliton Potential and Extended KdV Integer Solitons