Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Ernie G. Kalnins"'
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:
SIGMA 8 (2012), 034, 25 pages
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:
http://arxiv.org/abs/1202.0197
Publikováno v:
Physics of Atomic Nuclei. 70:576-583
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 m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::59d15d820a540a6e7ace4919e2603cd0
https://doi.org/10.1134/s1063778807030192
https://doi.org/10.1134/s1063778807030192
Classical (maximal) superintegrable systems in n dimensions are Hamiltonian systems with 2n−1 independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved algebraically. In thi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c64adb22be1515cd6c8271921a7ed4e
Publikováno v:
Physics of Atomic Nuclei. 68:1756-1763
We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schrodinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calcul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d80403c93a49c801b908c0a205ffa2fe
https://doi.org/10.1134/1.2121926
https://doi.org/10.1134/1.2121926
Autor:
Jonathan M. Kress, Ernie G. Kalnins
Publikováno v:
Physics of Atomic Nuclei. 65:1047-1051
In complex two-dimensional Euclidean space, the Hamilton-Jacobi or Schrodinger equation with a given “nondegenerate” potential is maximally superintegrable if and only if it is separated in more than one coordinate system. A similar statement for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c9d8ffb916b54fb5b867e402365eebaf
https://doi.org/10.1134/1.1490109
https://doi.org/10.1134/1.1490109
Publikováno v:
Journal of Physics A: Mathematical and General. 35:4755-4773
We give a graphical prescription for obtaining and characterizing all separable coordinates for which the Schr?dinger equation admits separable solutions for one of the superintegrable potentials Here xn+1 is a distinguished Cartesian variable. The a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::47c307f31eca8e6eaffecde6764838ca
https://doi.org/10.1088/0305-4470/35/22/308
https://doi.org/10.1088/0305-4470/35/22/308
Publikováno v:
Journal of Mathematical Physics. 43:970-983
A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b7f325dce09a163741f046f53dff313
https://doi.org/10.1063/1.1429322
https://doi.org/10.1063/1.1429322