Zobrazeno 1 - 10
of 38
pro vyhledávání: '"SłAWIANOWSKI, J. J."'
We are going to prove that the phase-space description is fundamental both in the classical and quantum physics. It is shown that many problems in statistical mechanics, quantum mechanics, quasi-classical theory and in the theory of integrable system
Externí odkaz:
http://arxiv.org/abs/1404.2588
Publikováno v:
Mathematical Methods in the Applied Sciences 35 (2012), 17-42
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, th
Externí odkaz:
http://arxiv.org/abs/1012.5768
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss geometric
Externí odkaz:
http://arxiv.org/abs/1012.4926
Publikováno v:
Journal of Geometry and Symmetry in Physics, vol. 23, 2011, pp. 59-95
This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems. Below we spe
Externí odkaz:
http://arxiv.org/abs/1008.3074
Publikováno v:
Journal of Geometry and Symmetry in Physics, vol. 22, 2011, pp. 67-94
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used. Below we ex
Externí odkaz:
http://arxiv.org/abs/1008.0512
Publikováno v:
Journal of Geometry and Symmetry in Physics, vol. 21, 2011, pp. 61-94
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$ and its q
Externí odkaz:
http://arxiv.org/abs/1007.4121
Autor:
Sławianowski, J. J., Gołubowska, B.
Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of structured
Externí odkaz:
http://arxiv.org/abs/0912.4606
Publikováno v:
Acta Physica Polonica B, vol. 41, no. 1, 2010, pp. 165-218
Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on some invariance properties under the action of isometric and affine trans
Externí odkaz:
http://arxiv.org/abs/0901.0243
Autor:
Sławianowski, J. J., Kovalchuk, V.
Publikováno v:
Reports on Mathematical Physics, vol. 65, no. 1, 2010, pp. 29-76.
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of "m
Externí odkaz:
http://arxiv.org/abs/0812.5055
Autor:
Sławianowski, J. J.
Publikováno v:
International Journal of Theoretical Physics, 44, no. 11, 2005, pp. 2029-2039
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in nuclear and hadr
Externí odkaz:
http://arxiv.org/abs/0802.3126