Integrable and Superintegrable Systems book.
Integrable and Superintegrable Systems book. Some of the most active practitioners in the field.
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Integrable And Superintegrable Systems
Integrable And Superintegrable Systems. Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
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They include integrable, superintegrable and maximally superintegrable systems. Among them is a system invariant with respect to the Lie algebra of Lorentz group and a system whose integrals of motion form algebra so(4). Three of the obtained systems are solved exactly. A system is superintegrable if one could obtain more than N constants of the motion and if there exist 2N-1 constants of the motion, the system is maximally superintegrable or just superintegrable provided that the commutator of operators as constants of the motion be zero with Hamiltonian of the system.
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In the context of differential equations to integrate an equation means to solve it from initial conditions
In the context of differential equations to integrate an equation means to solve it from initial conditions. Accordingly, an integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions. Many systems of differential equations arising in physics are integrable. A standard example is the motion of a rigid body about its center of mass
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space.
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. Contrary to the case of purely scalar potentials, quadratic integrability does not imply separation of variables in the Schroedinger equation. Moreover, quantum and classical integrable systems do not necessarily coincide: the Hamiltonian can depend on the Planck constant in a nontrivial manner. urn:arXiv:math-ph/0311051.
Электронная книга "Elements of Superintegrable Systems: Basic Techniques and Results", B. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Elements of Superintegrable Systems: Basic Techniques and Results" для чтения в офлайн-режиме.