Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
The N-dimensional Hamiltonianis shown to be quasi-maximally superintegrable for any
choice of the functions f and U. This result is proven by making use of the underlying sl (2, R) …
choice of the functions f and U. This result is proven by making use of the underlying sl (2, R) …
A maximally superintegrable system on an n-dimensional space of nonconstant curvature
We present a novel Hamiltonian system in n dimensions which admits the maximal number
2n− 1 of functionally independent, quadratic first integrals. This system turns out to be the …
2n− 1 of functionally independent, quadratic first integrals. This system turns out to be the …
Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries
EG Kalnins, W Miller, GS Pogosyan - Journal of mathematical physics, 2006 - pubs.aip.org
We show that second-order superintegrable systems in two-dimensional and three-
dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly …
dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly …
Asymptotically isochronous systems
F Calogero, D Gómez-Ullate - Journal of Nonlinear Mathematical …, 2008 - Taylor & Francis
Mechanisms are elucidated underlying the existence of dynamical systems whose generic
solutions approach asymptotically (at large time) isochronous evolutions: all their dependent …
solutions approach asymptotically (at large time) isochronous evolutions: all their dependent …
[图书][B] Quantum versus Classical Mechanics and Integrability Problems
M Błaszak - 2019 - Springer
It is well known for physicists that in order to describe dynamical systems of finite number of
degrees of freedom in the macro-and micro-scale, classical and quantum mechanics …
degrees of freedom in the macro-and micro-scale, classical and quantum mechanics …
On the quantum spectrum of isochronous potentials
J Dorignac - Journal of Physics A: Mathematical and General, 2005 - iopscience.iop.org
In this paper, the quantum spectrum of isochronous potentials is investigated. Given that the
frequency of the classical motion in such potentials is energy independent, it is natural to …
frequency of the classical motion in such potentials is energy independent, it is natural to …
Maximal superintegrability of Benenti systems
M Blaszak, A Sergyeyev - arXiv preprint nlin/0412018, 2004 - arxiv.org
arXiv:nlin/0412018v1 [nlin.SI] 6 Dec 2004 Maximal superintegrability of Benenti systems Page
1 arXiv:nlin/0412018v1 [nlin.SI] 6 Dec 2004 Maximal superintegrability of Benenti systems …
1 arXiv:nlin/0412018v1 [nlin.SI] 6 Dec 2004 Maximal superintegrability of Benenti systems …
[HTML][HTML] Global versus local superintegrability of nonlinear oscillators
Liouville (super) integrability of a Hamiltonian system of differential equations is based on
the existence of globally well-defined constants of the motion, while Lie point symmetries …
the existence of globally well-defined constants of the motion, while Lie point symmetries …
Classical and quantum superintegrability of Stäckel systems
M Błaszak, K Marciniak - SIGMA. Symmetry, Integrability and Geometry …, 2017 - emis.de
In this paper we discuss maximal superintegrability of both classical and quantum Stäckel
systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be …
systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be …
Quantum deformations and superintegrable motions on spaces with variable curvature
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-
3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians …
3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians …