A nonseparable quantum superintegrable system in 2D real Euclidean space

Abstract

In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second order integrals of motion but does admit one third and one fourth order integral. We also obtain a classical superintegrable system with the same properties. The quantum system differs from the classical one by corrections proportional to ${\hslash }^2.$

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• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
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• Transformation of the Stackel matrices preserving superintegrability
• Quantum, classical symmetries and action-angle variables by factorization of superintegrable systems
• On higher-dimensional superintegrable systems: A new family of classical and quantum Hamiltonian models
• Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity
• From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics
• Cubic first integrals of autonomous dynamical systems in $E^2$ by an algorithmic approach
• Jacobi last multiplier and two-dimensional superintegrable oscillators
• Integrable systems in magnetic fields: the generalized parabolic cylindrical case