Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion

Details Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion

2009-08-09

arxiv.org/abs/0908.1246v2

J.Math.Phys.50:122102,2009

Physics

Mathematical Physics

16 pages

Scientific paper

10.1063/1.3272003

The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric quantum mechanics. We obtain a new superintegrable potential separable in Cartesian coordinates with a quadratic and quintic integrals and also one with a quadratic integral and an integral of order seven. We also construct a superintegrable system written in terms of the fourth Painleve transcendent with a quadratic integral and an integral of order seven.

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