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Physics Bulletin

Formulations of Classical and Quantum Dynamical Theory

P. F. Dhooghe

Published Oct 1, 1970• 18 citations
Publisher

Abstract

G Rosen London: Academic Press 1970 pp xii + 151 price £4 9s Professor Rosen's monograph, valuable to senior undergraduate and graduate students in physics and mathematics, presents a clear and fundamental review of the mathematical structure and logical relationships between classical dynamics and quantum dynamics for nondissipative closed physical systems. The monograph is based upon the notes from a course of lectures given to seniors and graduate students.

DOI
10.1088/0031-9112/21/10/029

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G Rosen London: Academic Press 1970 pp xii + 151 price £4 9s Professor Rosen's monograph, valuable to senior undergraduate and graduate students in physics and mathematics, presents a clear and fundamental review of the mathematical structure and logical relationships between classical dynamics and quantum dynamics for nondissipative closed physical systems. The monograph is based upon the notes from a course of lectures given to seniors and graduate students.
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The ideal text for a two-semester graduate course on quantum mechanics. Fresh, comprehensive, and clear, it strikes the optimal balance between covering traditional material and exploring contemporary topics. Focusing on the probabilistic structure of quantum mechanics and the central role of symmetries to unify principles, this textbook guides readers through the logical development of the theory. Students will also learn about the more exciting and controversial aspects of quantum theory, with discussions on past interpretations and the current debates on cutting-edge concepts such as quantum information and entanglement, open quantum systems, and quantum measurement theory. The book has two types of content: Type A material is more elementary and is fully self-contained, functioning like a separate book within the book, while Type B content is at the level of a graduate course. Requiring minimal physics background, this textbook is appropriate for mathematics and engineering students, in addition to physicists. Introducing cutting-edge topics in the field, the book features about 150 concept-checking questions, 300 homework problems and a solutions manual.
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on mathematically precise formulations, the book summarises the relevant mathematics.