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

@article{Marquette2009SupersymmetryAA, title={Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion}, author={Ian Marquette}, journal={Journal of Mathematical Physics}, year={2009}, volume={50}, pages={122102-122102} }

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 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 of 7. We also construct a superintegrable system written in terms of…

## 45 Citations

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