Classical Systems in Quantum Mechanics

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems - i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of "quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

Auteur
Pavel Bona worked, until his recent retirement, as teacher and theoretician in the Department of Theoretical Physics within the Faculty of Mathematics, Physics and Informatics at Comenius University, Bratislava. He continues to publish and research in the field of quantum theory as applied also to macroscopic systems.

Contenu

Introduction.- Geometry of the state space of quantum mechanics.- Classical projections of quantum mechanics.- Examples of classical projections.- Macroscopic limits.- Mathematical structure of QM mean-fi eld theories.- Some models of "quantum measurement".