Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents

DOI: 10.4236/jamp.2014.211113   PDF   HTML     3,100 Downloads   3,462 Views  

Abstract

This article concerns the quantum superintegrable system obtained by Tremblay and Winternitz, which allows the separation of variables in polar coordinates and possesses three conserved quantities with the potential described by the sixth Painlevé equation. The degeneration procedure from the sixth Painlvé equation to the fifth one yields another new superintegrable system; however, the Hermitian nature is broken.

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Sasaki, Y. (2014) Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents. Journal of Applied Mathematics and Physics, 2, 996-999. doi: 10.4236/jamp.2014.211113.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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