Superintegrability in Classical and Quantum Systems

Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec). The meeting brought together scientists working in the area of finite-dimensional integrable systems to discuss new developments in this active field of interest. Properties possessed by these systems are manifold. In classical mechanics, they have stable periodic orbits (all finite orbits are periodic). In quantum mechanics, all known superintegrable systems have been shown to be exactly solvable. Their energy spectrum is degenerate and can be calculated algebraically.The spectra of superintegrable systems may also have other interesting properties, for example, the saturation of eigenfunction norm bounds. Articles in this volume cover several (overlapping) areas of research, including: standard superintegrable systems in classical and quantum mechanics; superintegrable systems with higher-order or nonpolynomial integrals; new types of superintegrable systems in classical mechanics; superintegrability, exact and quasi-exact solvability in standard and PT-symmetric quantum mechanics; quantum deformation, Nambu dynamics and algebraic perturbation theory of superintegrable systems; and, computer assisted classification of integrable equations. The volume is suitable for graduate students and research mathematicians interested in integrable systems.