Event
Adrian Escobar Ruiz, CRM, UdeM
Tuesday, November 7, 2017 15:30to16:30
Room 4336, Pav. Andr茅-Aisenstadt, 2920, ch. de la Tour, CA
Title: Fourth order superintegrable systems separating in Polar Coordinates: Exotic Potentials.
We present all real superintegrable quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schr枚dinger equation in polar coordinates, 2. They admit an independent fourth order integral of motion, 3. The angular dependent part of the potential satisfies a nonlinear ODE that has the Painlev茅 property and its solutions can be expressed in terms of the Painlev茅 transcendent P6. We also discuss the corresponding classical analogs of these potentials as well as the algebra of the integrals of motion.