rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Quantum versus Classical Mechanics and Integrability Problems
    sub title: towards a unification of approaches and tools
  name:
    name part: Błaszak, Maciej.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 460 p. online resource.
  abstract: 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: Introduction -- Basic Mathematical Tools -- Classical Hamiltonian Mechanics -- Classical Integrable and Separable Hamiltonian Systems -- Classical Separability Theory -- Deformation Theory of Classical Poisson Algebras -- Quantum Hamiltonian Mechanics on Symplectic Manifolds -- Position Representation of Quantum Mechanics over Riemannian Configuration Space -- References -- Index.
  note: by Maciej Błaszak.
  subject:
    topic: Quantum physics
  subject:
    topic: Mathematical physics
  subject:
    topic: Mechanics
  subject:
    topic: Quantum Physics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Classical Mechanics
  classification: QC173.96-174.52
  classification: 530.12
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783030183790
  identifier: https://doi.org/10.1007/978-3-030-18379-0
  record info:
    record creation date: 190611
    record change date: 20191026082023.0
    record identifier: 978-3-030-18379-0