The Dunkl oscillator on a space of nonconstant curvature: an exactly solvable quantum model with reflections

DOI10.1016/J.AOP.2023.169543arXiv2212.13575MaRDI QIDQ6183973

H. Panahi, Shi-Hai Dong, Hassan Hassanabadi, A. Najafizade, Ángel Ballesteros

Publication date: 5 January 2024

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.13575

zbMATH Keywords

curvatureexact solutionsLandau levelsintegrable deformationDunkl derivativeDarboux III oscillator

Mathematics Subject Classification ID

Derivative-free methods and methods using generalized derivatives (90C56) Estimates of eigenvalues in context of PDEs (35P15) Atomic physics (81V45) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37) Electro- and magnetostatics (78A30) Deformations and infinitesimal methods in commutative ring theory (13D10) Quasilinear elliptic equations with mean curvature operator (35J93) Special quantum systems, such as solvable systems (81Q80)

Cites Work

• Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform
• Supersymmetry without Hermiticity within \(\mathcal{PT}\) symmetric quantum mechanics

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