Classical Dynamics And Its Quantum Analogues (lecture Notes In Physics)

The primary purpose of this textbook is to introduce students to the principles of classical dynamics of particles, rigid bodies, and continuous systems while showing their relevance to subjects of contemporary interest. Two of these subjects are quantum mechanics and general relativity. The book shows in many examples the relations between quantum and classical mechanics and uses classical methods to derive most of the observational tests of general relativity. A third area of current interest is in nonlinear systems, and there are discussions of instability and of the geometrical methods used to study chaotic behaviour. In the belief that it is most important at this stage of a student's education to develop clear conceptual understanding, the mathematics is for the most part kept rather simple and traditional. In the belief that a good education in physics involves learning the history of the subject, this book devotes some space to important transitions in dynamics: the development of analytical methods in the 18th century and the invention of quantum mechanics. The distinctive contribution of this book is that it presents a pragmatic approach for preserving biological diversity. Experts in a wide variety of fields, including philosophy, environmental policy, law, economics and biology, present different perspectives on how to prevent widespread extinction around the world. Several chapters deal with basic questions such as how we should define biodiversity and how we should determine what is most important to save. Two chapters focus on how we can place an economic value on biological diversity, a step that is often critical for gaining acceptance for conservation efforts. One of the major conclusions is that people are often willing to pay to preserve natural systems that have no immediate value in terms of generating income or commodities. Other chapters are case studies of efforts to protect particular species or ecosystems; these provide practical guidelines for how to protect biodiversity more effectively. The book is divided into three sections: we start with discussions of efforts to protect endangered species; move to approaches for protecting intact, functioning natural ecosystems; and finish with proposals to protect the global natural system (the biosphere). It becomes clear as one progresses through these sections that these three approaches do not constitute distinctly different, much less competing, strategies for protecting biological diversity. Instead they are interdependent. Efforts to protect a particular endangered species typically lead to efforts to protect its ecosystem. Similarly, efforts to protect an ecosystem lead naturally to concerns about the atmosphere, climate and water supplies. The interdependence may also work in the other direction: loss of species potentially can undermine the stability and resilience of ecosystems, which can have a large negative impact on the biosphere. The main conclusion is that a wide range of approaches to conservation is needed to maintain diverse and ecologically functioning natural systems The Goodwin-Niering Center for Conservation Biology and Environmental Studies at Connecticut College is a comprehensive, interdisciplinary program that builds on one of the nation's leading undergraduate environmental studies programs. The C- ter fosters research, education, and curriculum development aimed at understanding contemporary ecological challenges. One of the major goals of the Goodwin-Niering Center is to enhance the understanding of both the College community and the general public with respect to ecological, political, social, and economic factors that affect natural resource use and preservation of natural ecosystems. To this end, the C- ter has offered six conferences at which academicians, representatives of federal and state government, people who depend on natural resources for their living, and in- viduals from non-government environmental organizations were brought together for an in-depth, interdisciplinary evaluation of important environmental issues. On April 6 and 7, 2007, the Center presented the Elizabeth Babbott Conant interdisciplinary conference on Saving Biological Diversity: Weighing the Protection of Endangered Species vs. Entire Ecosystems. The Beaver Brook Foundation; Audubon Connecticut, the state of?ce of the National Audubon Society; the Connecticut Chapter of The Nature Conservancy; Connecticut Forest and Park Association and the Connecticut Sea Grant College Program joined the Center as conference sponsors. During this two-day conference we learned about conservation and endangered species fromawiderange ofperspectives. Likeallof theconferences sponsored bythe Goodwin-Niering Center, this conference was broadly interdisciplinary, with pres- tations by economists, political scientists, and conservation biologists. The short Heroic Age of physics that started in 1925 was one of the rare occasions when a deep consideration of the What does physics really say? was necessary in carrying out numerical calculations. In many parts of microphysics the calculations have now become relatively straightforward if not easy, but most physicists seem to agree that some questions of principle remain to be resolved, even if they do not think it is very important to do so. This situation has affected the way people think and write about quantum mechanics, a gingerly approach to fundamentals and a tendency to emphasize what fifty years ago was new in the new theory at the expense of continuity with what came before it. Nowadays those who look into the subject are more likely to be struck by unexpected similarities between quantum and classical mechanics than by dramatic contrasts they had been led to expect. It is often said that the hardest part of understanding quantum mechanics is to understand that there is nothing to understand; all the same, to think quantum mechanically it helps to have firm mental connections with classical physics and to know exactly what these connections do and do not imply. This book originated more than a decade ago as informal lecture notes [OP, prepared for use in a course taught from time to time to advanced undergraduates at Williams College. Front Matter......Page 1 01 Rays of light......Page 8 02 Orbits of particles......Page 45 03 N-particle systems......Page 96 04 Hamiltonian dynamics......Page 118 05 The Hamilton-Jacobi theory......Page 158 06 Action and phase......Page 199 07 Theory of perturbations......Page 236 08 The motion of a rigid body......Page 264 09 Continuous systems......Page 309 Back Matter......Page 343 David Park. Includes Index. Bibliography: P. 336-339.