Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator

Abstract

We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyl's one, does not.

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• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Quantum integrability of quadratic Killing tensors
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• The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
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Cited by in corpus (1)

• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion