Speaker
Dr
Adrian Escobar
(CRM, University of Montreal)
Description
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables in polar coordinates, 2. They allow an independent fourth order integral of motion, 3. Their angular component $S(\theta)$ does not satisfy any linear ODE. We show that $S(\theta)$ satisfies a nonlinear ODE that has the Painlevé property. The classical analog, including the generating algebra of the integrals of motion, is considered as well.
Author
Dr
Adrian Escobar
(CRM, University of Montreal)
Co-authors
Dr
Juan Carlos Vieyra
(CRM University of Montreal)
Prof.
Pavel Winternitz
(CRM, University of Montreal)
