Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials

Details Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials

2009-01-20

arxiv.org/abs/0901.3081v1

SIGMA 5 (2009), 008, 24 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2009.008

The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is St\"ackel equivalent to a system on a constant curvature space.

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