Synopsis
In the past 10 to 15 years, the quantum leap in understanding of nonlinear dynamics has radically changed the frame of reference of physicists contemplating such systems. This book treats classical and quantum mechanics using an approach as introduced by nonlinear Hamiltonian dynamics and path integral methods. It is written for graduate students who want to become familiar with the more advanced computational strategies in classical and quantum dynamics. Therefore, worked examples comprise a large part of the text. While the first half of the book lays the groundwork for a standard course, the second half, with its detailed treatment of the time-dependent oscillator, classical and quantum Chern-Simons mechanics, the Maslov anomaly and the Berry phase, will acquaint the reader with modern topological methods that have not as yet found their way into the textbook literature.
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Review
From the reviews of the third edition:
"This book is a brilliant exposition of dynamical systems covering the essential aspects and written in an elegant manner. The book is written in modern language of mathematics and will ideally cater to the requirements of graduate and first year Ph.D. students...a wonderful introduction to any student who wants to do research in any branch of theoretical Physics."
--Indian Journal of Physics
"The point which makes this book really unique is the abundance of detailed well-chosen examples illustrating the action principle, the canonical transformations, the perturbation theory, and the removal of resonances...Numerous explicit examples of direct evaluations of path integrals make this approach particularly clear and attractive. This book will be of interest to both graduate and post-graduate advanced physics students and is warmly recommended in view of its originality and readability."
--Physicalia
"The search of possible connections between classical dynamics and quantum mechanics is an old exciting problem. ... The present book highlights the principle of stationary action as common starting point of both theories. ... This third edition ... is supplemented with chapters on the action principle in classical electrodynamics (an excellent example of working scheme), on the functional derivative approach and on computing traces in the context of WKB propagator. Extensive additions and detailed treatments are also included in the text." (Mircea Crâsmareanu, Zentralblatt MATH, Vol. 990 (15), 2002)
From the Back Cover
Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, together with many worked examples throughout the text.
This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.
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Advanced Classical and Quantum Dynamics
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Advanced Classical and Quantum Dynamics
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