Classical Mechanics And Relativity Second Edition

The text covers the entire domain of basic classical mechanics and relativity theory (special and general) and has been revised mainly for the purpose of adding exercises without worked solutions that were missing in the first edition. To retain the format of a readable, yet advanced introductory text that can serve as the companion text for a course in mechanics, the more than 100 new exercises on diverse topics are of moderate range; answers are given and occasionally hints are provided. As before, the text aims to cover the entire spectrum of theoretical mechanics from Newton to Einstein. The reader can observe how in the course of time, deeper and deeper insights were achieved with the development of the basic equations of Newton to those of Euler and Lagrange, and to the geodesic equations of space-time and Einstein's relativity. To include diverse problems, a small section on this topic has been added.

This book is a revised and updated version of Introductory Quantum Physics and Relativity. Based on lectures given as part of the undergraduate degree programme at the University of Leeds, it has been extended in line with recent developments in the field. The book contains all the material required for quantum physics and relativity in the first three years of a traditional physics degree, in addition to more interesting and up-to-date extensions and applications which include quantum field theory, entanglement, and quantum information science. The second edition is unique as an undergraduate textbook as it combines quantum physics and relativity at an introductory level. It expounds the foundations of these two subjects in detail, but also illustrates how they can be combined. It discusses recent applications, but also exposes undergraduates to cutting-edge research topics, such as laser cooling, Bose-Einstein condensation, tunneling microscopes, lasers, nonlocality, and quantum teleportation. Contents: IntroductionOld Quantum TheoryQuantum MechanicsApplications of Quantum MechanicsSchrödinger Equation in Three DimensionsSpin and StatisticsAtoms, Molecules and LasersFormal Structure of Quantum MechanicsSecond Revolution: RelativityFine Structure of the Hydrogen AtomRelativistic Quantum MechanicsQuantum EntanglementSolutions Readership: Students taking undergraduate-level courses in quantum physics and relativity. Keywords: Quantum Physics;RelativityReview: Key Features: Combines Quantum Physics and Relativity. Covers the two subjects in a more coherent way than existing books. Many universities teach quantum physics and relativity together as one lecture course and so a book that covers both but also shows how they can be combined is a valuable resourceModern Choice of Topics. We will draw on topics from our own research to bring the two subjects up to date and give students a taste of cutting edge research. Examples will include such things as laser cooling, Bose condensation, tunneling microscopes, lasers, Bell's inequalities, quantum teleportationHas questions and answers -- ideal for self-study. This is pitched at typical exam level and so will be excellent for exam practice

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.

Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogeneous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered. A tensor manipulation package to help students overcome the computational challenge associated with general relativity is available on a site hosted by the author. A link to this and to a solutions manual can be found at www.cambridge.org/9780521762458.

Applications not usually taught in physics courses include theory of space-charge limited currents, atmospheric drag, motion of meteoritic dust, variational principles in rocket motion, transfer functions, much more. 1960 edition.

Covariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.

This book provides a calculus-based perspective on classical mechanics and the theory of relativity. Unlike most conventional textbooks, the discussion on theory is pared down to a minimum in favor of detailed, guided solutions of problems illustrating salient points, subtleties and principles. By working through the 900 carefully selected problems, the serious learner will hence be stimulated, challenged and enlightened. Great emphasis is placed on the pedagogical value of solving problems in a number of ways, on the careful and detailed analysis of problems, on dimensional considerations, and on basic principles underlying every topic treated.The book is aimed at first-year undergraduate students in physics and engineering. Advanced Placement students in high schools will also find this book rewarding and challenging. Instructors too will be able to recharge their batteries and refresh their reservoir of problems for recitation classes, or delve into it for their own amusement and edification.