Zobrazeno 1 - 10
of 263
pro vyhledávání: '"Willard Miller"'
Publikováno v:
Acta Polytechnica, Vol 56, Iss 3, Pp 214-223 (2016)
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often ``hidden''.The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to defin
Externí odkaz:
https://doaj.org/article/d11772fa50c4482facae95b14ea4b58c
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 057 (2013)
We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions
Externí odkaz:
https://doaj.org/article/407a477b480b4242b5adc7ba88be7924
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 089 (2012)
Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems, namely Hami
Externí odkaz:
https://doaj.org/article/8e3d210b1a6e479f93a220cb93823111
Autor:
Ernie G. Kalnins, Willard Miller Jr.
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 034 (2012)
The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D
Externí odkaz:
https://doaj.org/article/061d5143ac194dd1b2dec1d7f21c6014
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 7, p 051 (2011)
We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). F
Externí odkaz:
https://doaj.org/article/e0ee419e78f44bbb8e74869942d1876f
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 7, p 031 (2011)
We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of
Externí odkaz:
https://doaj.org/article/628fd5ba9f404f9b91372160ab84b4b0
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 6, p 066 (2010)
Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, so that they are in fact su
Externí odkaz:
https://doaj.org/article/7515b864d361478ab0f03cce76038e96
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 5, p 008 (2009)
The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results
Externí odkaz:
https://doaj.org/article/c1da21cd506a45df94532fef1b194269
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 4, p 008 (2008)
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible representations o
Externí odkaz:
https://doaj.org/article/bc182cddcd65425f855e269a1a28626d
Autor:
Willard Miller
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 1, p 015 (2005)
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta, the maxim
Externí odkaz:
https://doaj.org/article/e3f94f56ac1847b0a614fce93c2df887