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Dynamical symmetries in physics
Hájek, Pavel ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
The aim of this thesis is to provide a definition of dynamical symme- try and to study its properties within simple quantum systems. In particular, I investigate Kepler's problem and the isotropic harmonic oscillator. Dynamical sy- mmetry is a kind of higher symmetry which is broken in a specific way. Definition of dynamical group and quantum mechanical system is presented. Subsequently, a definition of quantum degrees of freedom and quantum integrability is propo- sed. I mention briefly a possibility of finding the generators of dynamical group by considering time dependent constants of motion.
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Integrability in Hamiltonian machanics
Kokoška, David ; Krýsl, Svatopluk (advisor) ; Švarc, Robert (referee)
Title: Integrability in Hamiltonian mechanics Author: David Kokoška Department: Mathematical Institute of Charles University Supervisor: doc. RNDr. Svatopluk Krýsl, Ph.D., Mathematical Institute of Char- les University Abstract: Hamiltonian mechanics can be formulated using symplectic manifolds and so called Hamiltonian systems. In the Theorem of Liouville-Arnold, conditi- ons are described, under which solutions of Hamilton equations stay on a torus of dimension equal to the dimension of the configuration space. Examples on application of the Liouville-Arnold theorem are contained. We study the pro- blem of motion in a gravitational central force field in the connection with the Runge-Lenz vector. Keywords: symplectic manifold, hamiltonian system, Liouville-Arnold theorem, Kepler's problem 1
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Dynamical symmetries in physics
Hájek, Pavel ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
The aim of this thesis is to provide a definition of dynamical symme- try and to study its properties within simple quantum systems. In particular, I investigate Kepler's problem and the isotropic harmonic oscillator. Dynamical sy- mmetry is a kind of higher symmetry which is broken in a specific way. Definition of dynamical group and quantum mechanical system is presented. Subsequently, a definition of quantum degrees of freedom and quantum integrability is propo- sed. I mention briefly a possibility of finding the generators of dynamical group by considering time dependent constants of motion.
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