Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents
Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50964#.VFCKOlfHRK0 Author(s) Yoshikatsu Sasaki * Affiliation(s) Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan . 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. KEYWORDS ...