Author : Neumaier A., Westra D.
Description:Draft of a book, University of Vienna, 2011. 503 p. This book presents classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups.The book should serve as an appetizer, inviting the reader to go more deeply into these fascinating, interdisciplinary fields of science.Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics.We motivate everything as far as possible by classical mechanics. This forced an approach to quantum mechanics close to Heisenbergs matrix mechanics, rather than the usual approach dominated by Schrodingers wave mechanics. Indeed, although both approaches are formally equivalent, only the Heisenberg approach to quantum mechanics has any similarity with classical mechanics; and as we shall see, the similarity is quite close. Indeed, the present book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible