Foundations of Physics

, Volume 45, Issue 3, pp 253–278 | Cite as

Relations Between Different Notions of Degrees of Freedom of a Quantum System and Its Classical Model

  • Nikola BurićEmail author


There are at least three different notions of degrees of freedom (DF) that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the other to the structure of the system and the third to the properties of dynamical orbits. In this paper, definitions and comparison in classical and quantum systems of the tree types of DF are formulated and discussed. In particular, we concentrate on comparison of the number of the so called dynamical DF in a quantum system and its classical model. The comparison involves analyzes of relations between integrability of the classical model, dynamical symmetry and separability of the quantum and the corresponding classical systems and dynamical generation of appropriately defined quantumness. The analyzes is conducted using illustrative typical systems. A conjecture summarizing the observed relation between generation of quantumness by the quantum dynamics and dynamical properties of the classical model is formulated.


Degrees of freedom Generation of quantumness Hamiltonian dynamics 



This work was supported in part by the Ministry of Education and Science of the Republic of Serbia, under Project No. \(171017\)


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of BelgradeBelgradeSerbia

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