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The spherical version of the two-dimensional central harmonic oscillator, as well as the spherical Kepler (Schrödinger) potential, are superintegrable systems with quadratic constants of motion. They belong to two different spherical "Smorodinski-Winternitz" families of superintegrable potentials. A new superintegrable oscillator have been recently found in S². It represents the spherical version of the nonisotropic 2:1 oscillator and it also belongs to a spherical family of quadratic superintegrable...
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