Classical ladder operators, polynomial Poisson algebras and classification of superintegrable systems

Details Classical ladder operators, polynomial Poisson algebras and classification of superintegrable systems Classical ladder operators, polynomial Poisson algebras and classification of superintegrable systems

2011-09-21

arxiv.org/abs/1109.4471v2

J. Math. Phys. 53 012901 (2012)

Physics

Mathematical Physics

18 pages

Scientific paper

We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems respectively with a third and a fourth order ladder operators satisfying polynomial Heisenberg algebras. These systems are written in terms of the solutions of quartic and quintic equations. We use these results to present two new families of superintegrable systems and examples of trajectories that are deformed Lissajous's figures.

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