Periodic orbits for an infinite family of classical superintegrable systems

Details Periodic orbits for an infinite family of classical superintegrable systems Periodic orbits for an infinite family of classical superintegrable systems

2009-10-02

arxiv.org/abs/0910.0299v1

Physics

Mathematical Physics

16 pages, 14 figures

Scientific paper

We show that all bounded trajectories in the two dimensional classical system with the potential $V(r,\phi)=\omega^2 r^2+ \frac{\al k^2}{r^2 \cos^2 {k \phi}}+ \frac{\beta k^2}{r^2 \sin^2 {k \phi}}$ are closed for all integer and rational values of $k$. The period is $T=\frac{\pi}{2\omega}$ and does not depend on $k$. This agrees with our earlier conjecture suggesting that the quantum version of this system is superintegrable.

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