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(28) We have put the superscript ‘ ǫ’ in labelling the conserved quantities to remind the reader that they are obtained in the limit ω 1 ≈ ω 2

− 1 − ǫ 2 (p2 2 + q2 2), (27) where θj = − arctan ( pj qj ), we have used the fact that Xj = rj exp (iθj), Pj = − iX ∗ j to write Xj Pj = i exp (2iθj) = exp [ i ( π 2 + 2θj )]

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Dynamical symmetries of the anisotropic oscillator

math-ph · 2023-04-27 · unverdicted · novelty 6.0

Canonical transformations map the n-dimensional anisotropic oscillator to the isotropic oscillator, establishing maximal superintegrability for commensurate frequencies with explicit first integrals in 2D.

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  • Dynamical symmetries of the anisotropic oscillator math-ph · 2023-04-27 · unverdicted · none · ref 6

    Canonical transformations map the n-dimensional anisotropic oscillator to the isotropic oscillator, establishing maximal superintegrability for commensurate frequencies with explicit first integrals in 2D.