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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Quantum versus Classical Mechanics and Integrability Problems - towards a unification of approaches and tools (Hardcover, 1st ed. 2019)
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Quantum versus Classical Mechanics and Integrability Problems - towards a unification of approaches and tools (Hardcover, 1st ed. 2019)
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This accessible monograph introduces physicists to the general
relation between classical and quantum mechanics based on the
mathematical idea of deformation quantization and describes an
original approach to the theory of quantum integrable systems
developed by the author.The first goal of the book is to develop of
a common, coordinate free formulation of classical and quantum
Hamiltonian mechanics, framed in common mathematical language.In
particular, a coordinate free model of quantum Hamiltonian systems
in Riemannian spaces is formulated, based on the mathematical idea
of deformation quantization, as a complete physical theory with an
appropriate mathematical accuracy.The second goal is to develop of
a theory which allows for a deeper understanding of classical and
quantum integrability. For this reason the modern separability
theory on both classical and quantum level is presented. In
particular, the book presents a modern geometric separability
theory, based on bi-Poissonian and bi-presymplectic representations
of finite dimensional Liouville integrable systems and their
admissible separable quantizations.The book contains also a
generalized theory of classical Stackel transforms and the
discussion of the concept of quantum trajectories.In order to make
the text consistent and self-contained, the book starts with a
compact overview of mathematical tools necessary for understanding
the remaining part of the book. However, because the book is
dedicated mainly to physicists, despite its mathematical nature, it
refrains from highlighting definitions, theorems or
lemmas.Nevertheless, all statements presented are either proved or
the reader is referred to the literature where the proof is
available.
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