Analytical Mechanics for Relativity and Quantum Mechanics (Oxford Graduate Texts) 2nd Edition by Oliver Johns (PDF)

Description

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum mechanics: Part I is an introduction to analytical mechanics, suitable for a graduate or advanced undergraduate course. Part II presents material designed principally for graduate students. The appendices in Part III summarize the mathematical methods used in the text. The book integrates relativity into the teaching of classical mechanics. Part II introduces special relativity and covariant mechanics. It develops extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics, including an extended definition of canonical transformation that both simplifies the theory and no longer excludes the Lorentz transformation. The book assists students who study classical mechanics as a preparation for quantum mechanics. Analytical mechanics is presented using methods – such as linear vector operators and dyadics – that familiarize the student with similar operator techniques in quantum theory and the dyadic Dirac notation. Comparisons to quantum mechanics appear throughout the text. For example, the chapter on Hamilton-Jacobi theory includes discussions of the closely related Bohm hidden variable model and Feynman path integral method. The chapter on angle-action variables concludes with a section on the old quantum theory. Several of the fundamental problems in 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.New to the Second Edition:Part I contains new chapters on Central Force Motion (Chapter 11) and Scattering (Chapter 12), and new material on time-independent canonical transformations. Part II contains a new chapter (Chapter 22) on Angle-Action Variables. These additions allow a more flexible use of the text. Part I is now a self-contained, introductory analytical mechanics course. The instructor can then select a range of topics from Part II appropriate to the interests of more advanced students.

User’s Reviews

Editorial Reviews: Review 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 “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 About the Author Oliver Johns, Emeritus Professor, Department of Physics, San Francisco State UniversityOliver Davis Johns is Professor of Physics Emeritus at San Francisco State University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐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.

⭐This is an excellent book in the tradition of Lanczos’ classic work.I should have written it 20 years ago!

⭐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

⭐

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