Exact-Solvability of Superintegrable Systems

par Alexander Turbiner (ICN-UNAM, Mexico – Stony Brook Univ., USA – CRM, Canada)

lundi 2 nov. 2026, 14:00 → 15:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

All, so far known explicitly two-dimensional quantum superintegrable systems in flat space are exactly solvable with spectra linear in quantum numbers (in agreement with the Montreal Conjecture by Tempesta-Turbiner-Winternirz (2001)). Their eigenfunctions are bivariate orthogonal polynomials in invariants of the (discrete) symmetry group. It includes the Smorodinsky-Winternitz potentials I-IV (or the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero (equivalently, A₂ rational) and the Wolfes (equivalently, G₂ rational, or I₆) models, and the Tremblay-Turbiner-Winternitz system with integer index k=1,2,3,4. They have hidden (Lie) algebraic structure g^(k) with various k, and they possess a (finite order) polynomial algebras of integrals generated by the Hamiltonian, two algebraically-independent integrals and their commutator.

_____________________________________________________________

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe seminaire_physique PRENOM NOM"
(indiquez vos propres prénom et nom) et laissez le corps du message vide.