TITLE:
Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents
AUTHORS:
Yoshikatsu Sasaki
KEYWORDS:
Superintegrable System, Painlevé Equation, Degeneration
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.11,
October
28,
2014
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.