Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 081, 7 pages      arXiv:1606.06474      https://doi.org/10.3842/SIGMA.2016.081

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

Giovanni Rastelli
Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy

Received July 15, 2016, in final form August 15, 2016; Published online August 17, 2016

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.

Key words: Born-Jordan quantization; Weyl quantization; superintegrable systems; extended systems.

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