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
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Classical Systems in Quantum Mechanics
Classical Systems in Quantum Mechanics
Pavel Bóna
Classical Systems in Quantum Mechanics
123
Pavel Bóna Department of Theoretical Physics Comenius University Bratislava, Slovakia
ISBN 978-3-030-45069-4 ISBN 978-3-030-45070-0 https://doi.org/10.1007/978-3-030-45070-0
(eBook)
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Preface
The work contains a description and an analysis of two different approaches determining the connections between quantal and classical theories. The first approach associates with any quantum-mechanical system with a finite number of degrees of freedom a classical Hamiltonian system ‘living’ in projective Hilbert space PðHÞ, and it is called here the ‘classical projection’. The second approach deals with ‘large’ quantal (=quantum mechanical) systems in the limit of an infinite number of degrees of freedom and with their corresponding ‘macroscopic limits’ described as classical Hamiltonian systems of the system’s global (intensive) quantum observables. The last part of this work contains a series of models describing interactions of the “small” physical (micro) systems with the “macroscopic” ones, in which these interactions lead to a (macroscopic) change of some “classical” parameters of the large systems. These models connect, in a specific way, the two classes of the systems considered earlier in this work by modeling their mutual interactions leading to striking (i.e. theoretically impossible in the framework of finite quantum systems) results. The projective space PðHÞ of any complex Hilbert space H is endowed with a natural symplectic structure, which allows us to rewrite the quantum m
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