Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Chanu, Claudia Maria"'
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of arbitrarily high
Externí odkaz:
http://arxiv.org/abs/2411.19815
We study the degeneracy of the energy levels of the Schroedinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the Schwarzschild space-time respectively. Degeneracy of en
Externí odkaz:
http://arxiv.org/abs/2411.10824
Publikováno v:
SIGMA 19 (2023), 062, 18 pages
We introduce St\"ackel separable coordinates on the covering manifolds $M_k$, where $k$ is a rational parameter, of certain constant-curvature Riemannian manifolds with the structure of warped manifold. These covering manifolds appear implicitly in l
Externí odkaz:
http://arxiv.org/abs/2208.12690
Publikováno v:
SIGMA 16 (2020), 052, 16 pages
We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect analogy of
Externí odkaz:
http://arxiv.org/abs/2001.08613
The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of extension has
Externí odkaz:
http://arxiv.org/abs/2001.04152
Publikováno v:
SIGMA 15 (2019), 013, 22 pages
We study twisted products $H=\alpha^rH_r$ of natural autonomous Hamiltonians $H_r$, each one depending on a separate set, called here separate $r$-block, of variables. We show that, when the twist functions $\alpha^r$ are a row of the inverse of a bl
Externí odkaz:
http://arxiv.org/abs/1808.01889
Publikováno v:
Annals of Physics Volume 386, November 2017, Pages 254-274
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in
Externí odkaz:
http://arxiv.org/abs/1705.09519
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadrat
Externí odkaz:
http://arxiv.org/abs/1608.07243
Publikováno v:
SIGMA 11 (2015), 094, 9 pages
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm which com
Externí odkaz:
http://arxiv.org/abs/1509.07288
We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high deg
Externí odkaz:
http://arxiv.org/abs/1404.4825