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Superintegrable systems in classical and quantum mechanics. (English) Zbl 1064.35156
Shabat, A.B.(ed.) et al., New trends in integrability and partial solvability. Proceedings of the NATO Advanced Research Workshop, Cadiz, Spain, June 12–16, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1835-5/hbk). NATO Science Series II: Mathematics, Physics and Chemistry 132, 281-297 (2004).
Summary: A brief review is given of the status of superintegrability, i.e., the theory of classical and quantum mechanical finite-dimensional systems with more integrals of motion than degrees of freedom. Typically, in classical mechanics such systems are characterized by periodic motion, in quantum mechanics their energy levels can be calculated algebraically.
For the entire collection see [Zbl 1050.35003].

35Q40 PDEs in connection with quantum mechanics
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
70H05 Hamilton’s equations