My classmates & I hated this book when we took graduate mechanics. But three years later after struggling through Sakurai and Peskin & Schroeder I must admit this book gave me a solid grasp of Lagrangians and Hamiltonians. I would have often been lost without having studied this text first.In fact, Dr. Johns purposely designed this text on mechanics as a bridge to graduate quantum mechanics.
(After all, what other point is there to studying this subject at this level? The approach fails when things like friction come into play and if you want practical mechanics your time is better spent doing the computer problems in books like Fowler & Cassidy which are more realistic.)
Compared to Goldstein or Landau & Lifschitz it's a model of clarity and providing an appropriate level of support for first year grad students. The subject matter is hard, the problems are hard. They have to be if you want to learn physics at the graduate level. Five stars since there is nothing better for this level.
My only real complaint with the book is that the vast majority of my time solving the problems was spent doing very complicated algebra. Ten minutes of physics, hours of manipulating equations with page after page of algebra. Is it truly not possible to make difficult grad problems without spending most of your time on algebra? It makes impossible to use the answers in the back of the book because they take too long to see to completion.
Analytical Mechanics for Relativity and Quantum Mechanics (Oxford Graduate Texts) 2nd Edition
by
Oliver Johns
(Author)
ISBN-13: 978-0198567264
ISBN-10: 019856726X
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Analytical Mechanics for Relativity and Quantum Mechanics is 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.
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.
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Editorial Reviews
About the Author
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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Product details
- Publisher : Oxford University Press; 2nd edition (September 1, 2005)
- Language : English
- Hardcover : 626 pages
- ISBN-10 : 019856726X
- ISBN-13 : 978-0198567264
- Item Weight : 2.59 pounds
- Dimensions : 9.5 x 1.3 x 6.6 inches
- Customer Reviews:
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Reviewed in the United States on June 30, 2012
26 people found this helpful
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Reviewed in the United States on April 30, 2012
It's odd no one else has reviewed this book yet. I'm into the first few chapters, and I was looking up reviews to see if anyone had reviewed it yet. I've looked at a number of analytical mechanics books so far, including Lanczos * The Variational Principles of Mechanics, Fowles & Cassiday * Analytical Mechanics, and Landau, Lifshitz * Mechanics. The Landau is dense and starts right out on the first page with Lagrangians with no derivation or preparation. Lanczos has a slant toward variation, as the title suggests. I'm enjoying the Lanczos and will finish it. However, I wanted a more extensive treatment of analytical mechanics, and the Landau was daunting and isn't focused only on analytical mechanics. The Fowles and Cassiday is an undergraduate treatment that seemed too elementary. And so I settled on this fine Oxford hardback with the curious cover of an ancient king, which is very clear and easy to understand, with sufficient derivations, a number of exercises at the end of the chapter, and a mathematical appendix, which it must be admitted isn't very robust. But there are plenty of places to fill in your mathematics. Every fourth answer is in the back of the book. If you have a solid first couple of years of undergraduate physics and calculus, I think this is a fine place to learn your analytical mechanics. I also like the trajectory of the book: as the title suggests, the mechanics is pointed toward relativity and quantum mechanics, not classical mechanics. I suppose it's obvious I'm studying the book on my own. I teach AP Physics and AP Calculus in high school, and so I'm studying I suppose largely as a hobby. More later.
17 people found this helpful
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Reviewed in the United States on October 29, 2013
I am using this book as a reference/supplementary material for my undergraduate classical mechanics course. In my class we are using Marion & Thornton's Classical Dynamics of Particles and Systems as the major textbook. From time to time, my primary textbook's explanations on Lagrangian & Hamiltonian mechanics were a bit vague or insufficient. I found this book to be thorough enough to fill in the gaps in my understanding of Lagrangian & Hamiltonian mechanics, while being much more readable than Goldstein's Classical Mechanics for undergraduates like me. Only Part I of the book was relevant for my class until now, but now I am willing to study the rest of the book even if its contents are not part of my course.
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Top reviews from other countries
D. Cook
5.0 out of 5 stars
Just What I needed
Reviewed in the United Kingdom on May 30, 2013
This is an excellent book in the tradition of Lanczos' classic work.
I should have written it 20 years ago!
I should have written it 20 years ago!
Pirazzoli Silvano
4.0 out of 5 stars
Un esempio di come si scrive un buon testo di Meccanica
Reviewed in Italy on December 1, 2016
Un testo di ampio respiro, che sa essere rigoroso e discorsivo allo stesso tempo. E accessibile a chi abbia una base di Calcolo e Geometria Differenziale elementare

