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SUMMARY:Exact-Solvability of Superintegrable Systems
DTSTART:20261102T130000Z
DTEND:20261102T140000Z
DTSTAMP:20261110T125300Z
UID:indico-event-17644@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Alexander Turbiner (ICN-UNAM\, Mexico – Stony Broo
 k Univ.\, USA – CRM\, Canada)\n\nAll\, so far known explicitly two-dimen
 sional quantum superintegrable systems in flat space are exactly solvable 
 with spectra linear in quantum numbers (in agreement with the Montreal Con
 jecture 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 (equivalent
 ly\, A2 rational) and the Wolfes (equivalently\, G2 rational\, or I6) mode
 ls\, 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\, a
 nd they possess a (finite order) polynomial algebras of integrals generate
 d by the Hamiltonian\, two algebraically-independent integrals and their c
 ommutator.\n_____________________________________________________________\
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 indico.math.cnrs.fr/event/17644/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/17644/
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