Overview

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarize the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection. Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics.

Full Product Details

Author:   Oliver Johns (Emeritus Professor, Emeritus Professor, Department of Physics, San Francisco State University)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Edition:   2nd Revised edition
Dimensions:   Width: 17.80cm , Height: 3.70cm , Length: 24.40cm
Weight:   1.446kg
ISBN:  

9780191001628

ISBN 10:   0191001627
Pages:   652
Publication Date:   19 May 2011
Audience:   College/higher education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

I: INTRODUCTION: THE TRADITIONAL THEORY 1: Basic Dynamics of Point Particles and Collections 2: Introduction to Lagrangian Mechanics 3: Lagrangian Theory of Constraints 4: Introduction to Hamiltonian Mechanics 5: The Calculus of Variations 6: Hamilton's Principle 7: Linear Operators and Dyadics 8: Kinematics of Rotation 9: Rotational Dynamics 10: Small Vibrations About Equilibrium 11: Two-body Central Force Systems 12: Introduction to Scattering II:MECHANICS WITH TIME AS A COORDINATE 13: Lagrangian Mechanics with Time as a Coordinate 14: Hamiltonian Mechanics with Time as a Coordinate 15: Hamilton's Principle and Noether's Theorem 16: Relativity and Spacetime 17: Fourvectors and Operators 18: Relativistic Mechanics 19: Canonical Transformations 20: Generating Functions 21: Hamilton-Jacobi Theory III: MATHEMATICAL APPENDICES A: Vector Fundamentals B: Matrices and Determinants C: Eigenvalue Problem with General Metric D: The Calculus of Many Variables E: Geometry of Phase Space

Reviews

<br>Review from previous edition: <br> The author deserves to be congratulated on the production of what soon will establish itself as a well-respected and useful book which I am pleased to have on my shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject of analytical mechanics for relatively and quantum mechanics which would not benefit from use of this well-planned and conceived and refreshing presentation. --Current Engineering Practice <br><p><br> In recent years, there has been a tendency to eliminate the traditional Analytic Mechanics course from the graduate curriculum. One purpose of this book is to reverse this trend, to ensure that physics graduates learn their subject at the depth needed to advance beyond current thinking. Mathematical ReviewsR<p><br>

`Review from previous edition The author deserves to be congratulated on the production of what soon will establish itself as a well-respected and useful book which I am pleased to have on my shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject of analytical mechanics for relatively and quantum mechanics which would not benefit from use of this well-planned and conceived and refreshing presentation.' Current Engineering Practice

<br>Review from previous edition: <br> The author deserves to be congratulated on the production of what soon will establish itself as a well-respected and useful book which I am pleased to have on my shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject of analytical mechanics for relatively and quantum mechanics which would not benefit from use of this well-planned and conceived and refreshing presentation. --Current Engineering Practice <br><p><br>

Author Information

For the past 30 years, Professor Johns has taught graduate classical and quantum mechanics courses at San Francisco State University. This teaching experience has given him a sensitivity to the intellectual needs of physics graduate students. For the past fifteen years, he has had an association with the Department of Theoretical Physics at Oxford, making yearly visits. He does research in the foundations of physics: Hidden variable models, foundations of relativity, foundations of quantum mechanics. He has also done research work in theoretical Nuclear Physics and Nuclear Astrophysics, at the Niels Bohr Institute, Orsay, and the CEA laboratories in Paris.

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