3 edition of **Superintegrability in Classical and Quantum Systems (Crm Proceedings & Lecture Notes,)** found in the catalog.

- 382 Want to read
- 6 Currently reading

Published
**January 2004**
by American Mathematical Society
.

Written in

- Calculus & mathematical analysis,
- Mathematical Physics,
- Science

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 347 |

ID Numbers | |

Open Library | OL11420101M |

ISBN 10 | 0821833294 |

ISBN 10 | 9780821833292 |

Recently an interesting integrable two-dimensional model has attracted some attention, both on classical and quantum levels,,,. Its Hamiltonian reads (1) H = p r 2 + p φ 2 r 2 + ω 2 r 2 + α k 2 r 2 cos 2 (k φ) + β k 2 r 2 sin 2 (k φ), α, β > 0, where without loosing generality one can put k ⩾ 0. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stäckel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k.

Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. Abstract. A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals .

Abstract. In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to . Superintegrable systems of 1st order, i.e., classical systems where the dening symmetries are rst order in the momenta and quantum systems where the symmetries are rst order partial dierential operators, are directly related to Lie transformation groups and well understood.

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Buy Superintegrability in Classical and Quantum Systems (Crm Proceedings and Lecture Notes) on FREE SHIPPING on qualified ordersCited by: Abstract A brief review is given of the status of superintegrability, i.e., the theory of classical and quantum mechanical finite-dimensional systems with Cited by: 7.

Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).

A co-publication of the AMS and Centre de Recherches Mathématiques Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom.

Such systems have many interesting properties. Search for books, ebooks, a Workshop on Superintegrability in Classical and Quantum Systems |d ( |c Montréal, Québec) 1: 0 |a Superintegrability in classical and quantum systems / |c P.

Tempesta [et al.], editors. |a Providence. Abstract In this paper we discuss maximal superintegrability of both classical and quantum St\"{a}ckel systems.

We prove a sufficient condition for a flat or constant curvature St\"{a}ckel system. In quantum mechanics, superintegrability leads to an additional degeneracy of energy levels, sometimes called "accidental degeneracy". The term was coined by Fok and used by Moshinsky and collaborators, though the point of their studies was to show that this degeneracy is certainly no accident.

Superintegrability in Classical and Quantum Systems (CRM Proceedings and Lecture Notes) (vol ) [8] von Neumann J Mathematical Foundations of Quantum Mechanics vol 2 (Princeton, NJ: Princeton University Press). This book describes, Folding and Unfolding Classical and Quantum Systems.

José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi. like integrability and superintegrability, are deeply related to the previous development and will be covered in the last part of the book.

The mathematical framework used to present the previous. Classical and quantum superintegrability with applications To cite this article: Willard Miller Jr et al J.

Phys. A: Math. Theor. 46 View the article online for updates and enhancements. Related content Extended Kepler--Coulomb quantum superintegrable systems in three dimensions E G Kalnins, J M Kress and W Miller Jr.

ISBN: OCLC Number: Description: 1 online resource (x, pages): illustrations. Contents: 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.

The symmetries of the classical and quantum Fock–Darwin system are analyzed. For rational values of a relevant parameter γ, the quantum and classical FD systems are superintegrable. The effect of symmetries is shown in both classical and quantum frames. Coherent states are shown to relate classical and quantum motions.

A superintegrable system is one that has more integrals of motion than degrees of freedom. A maximally superintegrable system has 2n-1 integrals of motion, n of them in involution. In classical mechanics such systems have stable periodic orbits (all finite orbits are periodic).

In quantum mechanics all known superintegrable. Willard Miller Jr., Sarah Post, Pavel Winternitz A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta.

The integrals of motion of the classical two-dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable problem has a quantum counterpart, a quantum superintegrable system.

We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e., the potentials are proportional to ℏ 2, so their classical limit is free motion.

In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally superintegrable. Abstract We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties.

They are integrable because they allow the separation of. Superintegrability and higher-order constants for classical and quantum systems. Physics and Atomic Nuclei, 74(6), Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are.

fourth order quantum superintegrable systems were announced by Evans and Verrier [], and by Rodriguez, Tempesta, and Winternitz [, ]. Superintegrable systems of second-order, i.e., classical systems where the deﬁning sym-metries are second-order in the momenta and quantum systems where the symmetries are.

There are also exactly solvable models in statistical mechanics, which are more closely related to quantum integrable systems than classical ones. Two closely related methods: the Bethe ansatz approach, in its modern sense, based on the Yang–Baxter equations and the quantum inverse scattering method provide quantum analogs of the inverse.of a classical superintegrable system is the maximum order of the generating constants of the motion (with the Hamiltonian excluded) as a polynomial in the momenta, and the maximum order of the quantum symmetries as dierential operators.

Systems of 2nd order have been well.The Stäckel transform is a mapping of the commuting constants of the motion (corresponding to a separable coordinate system) for one completely integrable classical or quantum Hamiltonian system to the constants of the motion for another such system.

Here the transform is defined and given an intrinsic characterization, and a large family of nontrivial examples is worked out of systems which.