An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

Details An infinite family of superintegrable systems from higher order ladder operators and supersymmetry An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

2010-08-18

arxiv.org/abs/1008.3073v2

J.Phys.Conf.Ser.284:012047,2011

Physics

Mathematical Physics

8 pages, presented at ICGTMP 28, accepted for j.conf.series

Scientific paper

10.1088/1742-6596/284/1/012047

We will discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from ladder operators. We will discuss also how higher order supersymmetric quantum mechanics can be used to obtain systems with higher order ladder operators and their polynomial Heisenberg algebra. We will present a new family of superintegrable systems involving the fifth Painleve transcendent which possess fourth order ladder operators constructed from second order supersymmetric quantum mechanics. We present the polynomial algebra of this family of superintegrable systems.

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