# Classical Systems in Quantum Mechanics

@article{Bona2019ClassicalSI,
title={Classical Systems in Quantum Mechanics},
author={Pavel B'ona},
journal={arXiv: Mathematical Physics},
year={2019}
}
• Pavel B'ona
• Published 3 November 2019
• Physics
• arXiv: Mathematical Physics
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of kinematics and dynamics of classical systems emerges from the mathematical formalism of QM. The first of these ways is to obtain an equivalent description of QM (with finite number of degrees of freedom) as a classical Hamiltonian field theory and afterwards…
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## References

SHOWING 1-10 OF 164 REFERENCES

AbstractProposals for nonlinear extenstions of quantum mechanics are dis-cussed. Two diﬀerent concepts of “mixed state” for any nonlinear versionof quantum theory are introduced: (i) genuine mixture
• Physics, Philosophy
• 2009
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called
Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schrödinger equation and the absence of hidden variables. This leads
• Physics
• 1983
This volume presents the proceedings of a colloquium inspired by the former President of the French Mathematical Society, Michel Herve. The aim was to promote the development of mathematics through
The notion of a multiplier of a group X is generalized to that of a C*-multiplier by allowing it to have values in an arbitrary C*-algebra A. On the other hand, the notion of the action of X in A is

• 2000

• 1983

### Širaň: A Radiating Spin Chain as a Model of Irreversible Dynamics, Bratislava 2012, http://arxiv.org/abs/1211.6783

• 2012
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical