On the relation between superintegrability and exact solvability

Pavel Winternitz (wintern@crm.umontreal.ca)
Professor CRM et DMS,
Universite de Montréal
Centre de recherches mathématiques
Université de Montréal
C.P. 6128, succ. Centre Ville
Montréal, QC, H3C 3J7, Canada

Abstract

Maximally superintegrable systems with n degrees of freedom have 2n-1 integrals of motion. Exactly solvable systems in quantum mechanics are those for which the energy spectrum can be calculated algebraically. We conjecture and demonstrate on examples that these two concepts are correlated.