Quantum versus Classical Mechanics and Int...

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Beschreibung

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.

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.

The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.

Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Zusammenfassung

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

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2020
Fachbereich:	Theoretische Physik
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiii 460 S.
ISBN-13:	9783030183813
ISBN-10:	3030183815
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	B¿aszak, Maciej
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 26 mm
Von/Mit:	Maciej B¿aszak
Erscheinungsdatum:	14.08.2020
Gewicht:	0,715 kg