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Superintegrability in Classical and Quantum Systems
About this Title
P. Tempesta, Scuola Superiore Internazionale, Trieste, Italy, P. Winternitz, University of Montréal, Montréal, QC, Canada, J. Harnad, University of Montréal, Montréal, QC, Canada, W. Miller Jr., University of Minnesota, Minneapolis, MN, G. Pogosyan, Joint Institute of Theoretical Physics, Moscow, Russia and M. Rodriguez, Universidad Complutense de Madrid, Madrid, Spain, Editors
Publication: CRM Proceedings and Lecture Notes
Publication Year:
2004; Volume 37
ISBNs: 978-0-8218-3329-2 (print); 978-1-4704-3951-4 (online)
DOI: https://doi.org/10.1090/crmp/037
MathSciNet review: MR2105429
MSC: Primary 00B25; Secondary 37-06, 37J35, 70-06, 70H06, 81-06, 81R12
ReadershipTable of Contents
Front/Back Matter
Chapters
- Superintegrable deformations of the Smorodinsky–Winternitz Hamiltonian
- Isochronous motions galore: Nonlinearly coupled oscillators with lots of isochronous solutions
- Nambu dynamics, deformation quantization, and superintegrability
- Maximally superintegrable systems of Winternitz type
- Cubic integrals of motion and quantum superintegrability
- Superintegrability, Lax matrices and separation of variables
- Maximally superintegrable Smorodinsky–Winternitz systems on the $N$-dimensional sphere and hyperbolic spaces
- Invariant Wirtinger projective connection and Tau-functions on spaces of branched coverings
- Dyon-oscillator duality. Hidden symmetry of the Yang-Coulomb monopole
- Supersymmetric Calogero-Moser-Sutherland models: Superintegrability structure and eigenfunctions
- Complete sets of invariants for classical systems
- Higher-order symmetry operators for Schrödinger equation
- Symmetries and Lagrangian time-discretizations of Euler equations
- Two exactly-solvable problems in one-dimensional quantum mechanics on circle
- Higher-order superintegrability of a rational oscillator with inversely quadratic nonlinearities: Euclidean and non-Euclidean cases
- A survey of quasi-exactly solvable systems and spin Calogero–Sutherland models
- On the classification of third-order integrals of motion in two-dimensional quantum mechanics
- Towards a classification of cubic integrals of motion
- Integrable systems whose spectral curves are the graph of a function
- On superintegrable systems in $E_2$: Algebraic properties and symmetry preserving discretization
- Perturbations of integrable systems and Dyson-Mehta integrals
- Separability and the Birkhoff–Gustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials
- Integrability and superintegrability without separability
- Applications of CRACK in the classification of integrable systems
- The prolate spheroidal phenomenon as a consequence of bispectrality
- On a trigonometric analogue of Atiyah–Hitchin bracket
- Separation of variables in time-dependent Schrödinger equations
- New types of solvability in PT symmetric quantum theory