Solvable rational extensions of the Morse and Kepler-Coulomb potentials

Abstract

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-Bäcklund transformations based on unphysical regular Riccati-Schrödinger functions which are obtained from specific symmetries associated to the considered family of potentials.

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• Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators
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• Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
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• DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
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• Symmetries and the compatibility condition for the new translational shape invariant potentials
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• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
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