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Titlebook: Quantum versus Classical Mechanics and Integrability Problems; towards a unificatio Maciej Błaszak Book 2019 Springer Nature Switzerland AG

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Classical Hamiltonian Mechanics, mechanics. The theory is formulated in the frame of Poisson geometry and presymplectic geometry. On the level of statistical Hamiltonian mechanics we introduce the language and notions familiar from the quantum level in order to further unify both theories. In particular we consider such issues as
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Classical Integrable and Separable Hamiltonian Systems,sed on the notion of separation relations introduced by Sklyanin. Separation relations are the most fundamental objects of modern separability theory as well as allow for classification of all separable systems. We concentrate our attention on the subclass of separable systems for which all constant
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Position Representation of Quantum Mechanics over Riemannian Configuration Space,ction of the so called position representation of quantum mechanics over an appropriate class of Riemaniann spaces in any admissible local curvilinear coordinates. In particular, for a flat space and Cartesian coordinates we reconstruct the standard quantization procedure from textbooks of quantum m
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Position Representation of Quantum Mechanics over Riemannian Configuration Space,resent the reader a class of quantizations of classical Stäckel systems considered in previous chapters, which preserve quantum integrability, quantum superintegrability and quantum stationary separability of related quantum Hamiltonian operators.
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