A generalized quantum nonlinear oscillator

Abstract

We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the new exactly solvable potentials possess shape invariance symmetry. The solutions are obtained in terms of classical orthogonal polynomials.

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Cited by in corpus (19)

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• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
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• Algebraic solutions of shape-invariant position-dependent effective mass systems
• Quantum oscillator and Kepler-Coulomb problems in curved spaces: deformed shape invariance, point canonical transformations, and rational extensions
• A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
• On the complete integrability of a nonlinear oscillator from group theoretical perspective
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry
• 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
• Rational extension and Jacobi-type {\boldmath{$X_m$}} solutions of a quantum nonlinear oscillator
• On the classical and quantum dynamics of a class of nonpolynomial oscillators
• Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
• On the symmetries of a nonlinear non-polynomial oscillator
• Liénard Type Nonlinear Oscillators and Quantum Solvability
• Two-step Shape Invariance in the Framework of N-fold Supersymmetry
• Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum