Classical Systems in Quantum Mechanics
Abstract
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 restrict it in dependence of specific classical system to obtain the classical Hamiltonian mechanics of that system. The second way is transition to QM of systems with infinite number of degrees of freedom  i.e. of macroscopic systems  and extract from it classical mechanics (with finite number of degrees of freedom) of macroscopic variables of this quantum system. The last 7th chapter of the text contains some considerations concerning the "measurement problem in QM", in which a measured quantum "microsystem" has to be dynamically connected with changes of classical states of a macroscopic quantum (sub)system  the measuring device. Several models of this process are presented.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.02081
 Bibcode:
 2019arXiv191102081B
 Keywords:

 Mathematical Physics
 EPrint:
 book format, 226 pages, extensive bibliography and index, hypertext