Classical Systems in Quantum Mechanics, 1st ed. 2020

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".

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".

Addresses the knotty problem of the quantum-classical divide

Adopts two approaches for describing classical systems in the framework of quantum mechanics

Presents solvable models of the "quantum measurement" process