A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell

Abstract

We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors. In a certain limit, it reduces to a continuous \ell family of shape invariant potentials related to the exceptional (X_{\ell}) L1 Laguerre polynomials. The latter was known as one example of the `conditionally exactly solvable potentials' on a half line.

arXiv comment19 pages. Sec.5(Summary and Comments): one sentence added in the first paragraph, several sentences modified in the last paragraph. References: one reference ([25]) added

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Cited by in corpus (11)

• Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
• Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials
• Approximate Analytical Solutions to Relativistic and Nonrelativistic Pöschl-Teller Potential with its Thermodynamic Properties
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
• Scattering Amplitudes for Multi-indexed Extensions of Solvable Potentials
• DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
• Equivalences of the Multi-Indexed Orthogonal Polynomials
• Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics
• A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
• Symmetries and the compatibility condition for the new translational shape invariant potentials
• Non-polynomial extensions of solvable potentials a la Abraham-Moses