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Quantum versus Classical Mechanics and Integrability Problems

towards a unification of approaches and tools

Authors: Błaszak, Maciej

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  • Detailed presentation of an original approach to the theory of quantum integrable systems
  • With a broad introduction to the general relation between classical and quantum mechanics
  • Highlights Examples to illustrate the theory and Observations with the most important messages
  • Accessible to physicists as well as mathematicians
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-030-18379-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-18378-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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 Stäckel 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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-030-18379-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-18378-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum versus Classical Mechanics and Integrability Problems
Book Subtitle
towards a unification of approaches and tools
Authors
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-18379-0
DOI
10.1007/978-3-030-18379-0
Hardcover ISBN
978-3-030-18378-3
Edition Number
1
Number of Pages
XIII, 460
Topics