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pro vyhledávání: '"Santander, Mariano"'
Autor:
Santander, Mariano
Publikováno v:
Int.\ J.\ Geom.\ Methods Mod.\ Phys., {\bf 10}, 08 (September 2013) 1360002
This article contains the last part of the mini-course `Spaces: a perspective view' delivered at the IFWGP2012. Here I deal with the part of the mini-course which centers on the classification questions associated to the simple real Lie groups. I rev
Externí odkaz:
http://arxiv.org/abs/2208.14702
Publikováno v:
J. Phys. A : Math. Theor. vol. 54, 10, 105201 (2021)
We study four particular 3-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the maximal number of functionally independent integrals of motion. The tw
Externí odkaz:
http://arxiv.org/abs/2109.04937
Publikováno v:
J. Phys. A : Math. Theor. vol. 54, 36, 365201 (2021)
The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta. Then we st
Externí odkaz:
http://arxiv.org/abs/2109.03716
Publikováno v:
Geom. Integrability & Quantization vol. XX, I. Mladenov, V. Pulov and A. Yoshioka, eds. (Sofia: Avangard Prima, 2019) 161-183
The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a manner that t
Externí odkaz:
http://arxiv.org/abs/1812.11883
The quantization of systems with a position dependent mass (PDM) is studied. We present a method that starts with the study of the existence of Killing vector fields for the PDM geodesic motion (Lagrangian with a PDM kinetic term but without any pote
Externí odkaz:
http://arxiv.org/abs/1710.02135
Publikováno v:
J. Math. Phys. 53, 102109 (2012)
This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$
Externí odkaz:
http://arxiv.org/abs/1211.2076
Publikováno v:
J. Phys. A: Math. Theor. 45, 265303 (14pp) (2012)
A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($\kappa>0$) and $H_k^3$ ($\kappa<0$), is studied. The curvature $\k$ is considered as a parameter and then the radial S
Externí odkaz:
http://arxiv.org/abs/1210.5055
Publikováno v:
Journal of Mathematical Physics {\bf 52}, 072104 (2011)
The quantum free particle on the sphere $S_\kappa^2$ ($\kappa>0$) and on the hyperbolic plane $H_\kappa^2$ ($\kappa<0$) is studied using a formalism that considers the curvature $\k$ as a parameter. The first part is mainly concerned with the analysi
Externí odkaz:
http://arxiv.org/abs/1201.5589
Publikováno v:
J. Math. Phys., no. 4, 042901 (2010)
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean plane; th
Externí odkaz:
http://arxiv.org/abs/1002.3870
Publikováno v:
J. Math. Phys. {\bf 49, 032703 (2008)
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of
Externí odkaz:
http://arxiv.org/abs/0709.2572