Rational extension and Jacobi-type {\boldmath{$X_m$}} solutions of a quantum nonlinear oscillator

Abstract

We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type $X_m$ exceptional orthogonal polynomials.

To appear in Journal of Mathematical Physics

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Cited by in corpus (8)

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• Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators
• An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates
• Solutions to the Painlevé V equation through supersymmetric quantum mechanics
• On the classical and quantum dynamics of a class of nonpolynomial oscillators
• On the symmetries of a nonlinear non-polynomial oscillator
• Liénard Type Nonlinear Oscillators and Quantum Solvability