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}
}
  • I. Marquette
  • Published 9 August 2009
  • Mathematics, Physics
  • Journal of Mathematical Physics
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… 

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