Classical Systems in Quantum Mechanics
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Beschreibung
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".
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".
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
Autor*in
Pavel Bóna
Themen in »Classical Systems in Quantum Mechanics«
Transition from quantum to classical Symplectic geometry on P(H) Macroscopic systems in quantum mechanics C*- and W*-algebras and their representations Disjointness of states Infinite direct product Duals of Banach spaces Quantum theory of measurement