The Principles of Newtonian and Quantum Mechanics

The Need for Planck's Constant, h

Nonfiction, Science & Nature, Science, Physics, Mechanics, Quantum Theory
Cover of the book The Principles of Newtonian and Quantum Mechanics by Maurice A de Gosson, Basil Hiley, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Maurice A de Gosson, Basil Hiley ISBN: 9789813200982
Publisher: World Scientific Publishing Company Publication: November 10, 2016
Imprint: WSPC Language: English
Author: Maurice A de Gosson, Basil Hiley
ISBN: 9789813200982
Publisher: World Scientific Publishing Company
Publication: November 10, 2016
Imprint: WSPC
Language: English

The second edition of this book deals, as the first, with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the "principle of the symplectic camel", which is a deep topological property of Hamiltonian flows. We introduce the notion of "quantum blob", which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

Contents:

  • From Kepler to Schrödinger ... and Beyond

  • Newtonian Mechanics

  • The Symplectic Group

  • Action and Phase

  • Semi-Classical Mechanics

  • Metaplectic Group, Maslov Index and Quantization

  • Schrödinger's Equation and the Metatron

  • Appendices:

    • Symplectic Linear Algebra
    • The Lie-Trotter Formula for Flows
    • The Heisenberg Groups
    • The Bundle of s-Densities
    • The Lagrangian Grassmannian

Readership: Reserchers and graduate students in mathematical physics and physics.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The second edition of this book deals, as the first, with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the "principle of the symplectic camel", which is a deep topological property of Hamiltonian flows. We introduce the notion of "quantum blob", which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

Contents:

Readership: Reserchers and graduate students in mathematical physics and physics.

More books from World Scientific Publishing Company

Cover of the book Social Integration of Rural-Urban Migrants in China by Maurice A de Gosson, Basil Hiley
Cover of the book Matrix Calculus, Kronecker Product and Tensor Product by Maurice A de Gosson, Basil Hiley
Cover of the book A Guide to Mathematical Methods for Physicists by Maurice A de Gosson, Basil Hiley
Cover of the book Geometric Inequalities by Maurice A de Gosson, Basil Hiley
Cover of the book Mathematics, Poetry and Beauty by Maurice A de Gosson, Basil Hiley
Cover of the book Japan — Between Myth and Reality by Maurice A de Gosson, Basil Hiley
Cover of the book Advanced Materials, Technology and Application by Maurice A de Gosson, Basil Hiley
Cover of the book Beams and Accelerators with MATLAB by Maurice A de Gosson, Basil Hiley
Cover of the book A History of Food Culture in China by Maurice A de Gosson, Basil Hiley
Cover of the book Strong Coupling Gauge Theories in the LHC Perspective (SCGT12) by Maurice A de Gosson, Basil Hiley
Cover of the book World Scientific Handbook of Experimental Results on High Speed Penetration into Metals, Concrete and Soils by Maurice A de Gosson, Basil Hiley
Cover of the book Cosmic Paradoxes by Maurice A de Gosson, Basil Hiley
Cover of the book Querying and Mining Uncertain Data Streams by Maurice A de Gosson, Basil Hiley
Cover of the book The Neutrophils by Maurice A de Gosson, Basil Hiley
Cover of the book World Development and Economic Systems by Maurice A de Gosson, Basil Hiley
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy