Prepotential approach to solvable rational extensions of Harmonic Oscillator and Morse potentials

Abstract

We show how the recently discovered solvable rational extensions of Harmonic Oscillator and Morse potentials can be constructed in a direct and systematic way, without the need of supersymmetry, shape invariance, Darboux-Crum and Darboux-Bäcklund transformations

7 pages, no figures. Sect II considerably shortened, discussions on ground states added. Version to appear in J. Math. Phys

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Cited by in corpus (18)

• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
• Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators
• New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems
• Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
• Extensions of solvable potentials with finitely many discrete eigenstates
• Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
• Extending Romanovski polynomials in quantum mechanics
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
• Group theoretic approach to rationally extended shape invariant potentials
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
• Rational extension and Jacobi-type {\boldmath{$X_m$}} solutions of a quantum nonlinear oscillator
• Ladder operators for solvable potentials connected with exceptional orthogonal polynomials
• Symmetries and the compatibility condition for the new translational shape invariant potentials
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators