Published in 1934, this monograph was one of the first introductory accounts of the principles which form the physical basis of the Quantum Theory, considered as a branch of mathematics. The exposition is restricted to a discussion of general principles and does not attempt detailed application to the wide domain of atomic physics, although a number of special problems are considered in elucidation of the principles. The necessary fundamental mathematical methods – the theory of linear operators and of matrics – are developed in the first chapter so this could introduce anyone to the new theory. This is an interesting snapshot of scientific history.
Published in 1934, this monograph was one of the first introductory accounts of the principles which form the physical basis of the Quantum Theory, considered as a branch of mathematics. The exposition is restricted to a discussion of general principles and does not attempt detailed application to the wide domain of atomic physics, although a number of special problems are considered in elucidation of the principles. The necessary fundamental mathematical methods – the theory of linear operators and of matrics – are developed in the first chapter so this could introduce anyone to the new theory. This is an interesting snapshot of scientific history.
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.
A large body of mathematics consists of facts that can be presented and described much like any other natural phenomenon. These facts, at times explicitly brought out as theorems, at other times concealed within a proof, make up most of the applications of mathematics, and are the most likely to survive changes of style and of interest. This ENCYCLOPEDIA will attempt to present the factual body of all mathematics. Clarity of exposition, accessibility to the non-specialist, and a thorough bibliography are required of each author. Volumes will appear in no particular order, but will be organized into sections, each one comprising a recognizable branch of present-day mathematics. Numbers of volumes and sections will be reconsidered as times and needs change. It is hoped that this enterprise will make mathematics more widely used where it is needed, and more accessible in fields in which it can be applied but where it has not yet penetrated because of insufficient information. The present volume is meant to be the first of a series on quantum mechanics and its applications. It deals with the foundations as well as the fascinating logic of quantum mechanics. This volume is more general and at places less factual than other volumes of the ENCYCLOPEDIA; nevertheless the thorough presentation will guide the reader to gain an overview of a theory that, together with relativity, is regarded as the greatest achievement in physics in this century.
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.
Quantum theory, the most successful physical theory of all time, provoked intense debate between the twentieth century's two greatest physicists, Niels Bohr and Albert Einstein. Quantum information theory has emerged from intensive study of the structure and interpretation of quantum theory to become one of the fastest growing areas of twenty-first century science. This second edition has been extensively revised and updated to cover recent developments, including the findings of papers published since the well-received first edition. A substantial new chapter is devoted to the development and structure of quantum information theory. Developments in the experimental and theoretical study of Bell's Theorem are also covered in detail, and the accounts of ongoing work have been brought up to date. A fascinating account of the development of quantum theory, this book will appeal to anyone with an interest in the fundamental questions of physics, its philosophy and its history.
Offering a detailed account of the key concepts and mathematical apparatus of quantum mechanics, this textbook is an ideal companion to both undergraduate and graduate courses. The formal and practical aspects of the subject are explained clearly alongside examples of modern applications, providing students with the tools required to thoroughly understand the theory and apply it. The authors provide an intuitive conceptual framework that is grounded in a coherent physical explanation of quantum phenomena, established over decades of teaching and research in quantum mechanics and its foundations. The book's educational value is enhanced by the inclusion of examples and exercises, with solutions available online, and an extensive bibliography is provided. Notes throughout the text provide fascinating context on the tumultuous history of quantum mechanics, the people that developed it, and the questions that still remain at its center. This title is also available as Open Access on Cambridge Core.
This book provides a broad introductory survey of this remarkable field, aiming to establish and clearly differentiate its physical principles, and also to provide a snapshot portrait of many of the most prominent current applications. Primary emphasis is placed on developing an understanding of the fundamental photonic origin behind the mechanism that operates in each type of effect. To this end, the first few chapters introduce and develop core theory, focusing on the physical significance and source of the most salient parameters, and revealing the detailed interplay between the key material and optical properties. Where appropriate, both classical and photonic (quantum mechanical) representations are discussed. The number of equations is purposely kept to a minimum, and only a broad background in optical physics is assumed. With copious examples and illustrations, each of the subsequent chapters then sets out to explain and exhibit the main features and uses of the various distinct types of mechanism that can be involved in optical nanomanipulation, including some of the very latest developments. To complete the scene, we also briefly discuss applications to larger, biological particles. Overall, this book aims to deliver to the non-specialist an amenable introduction to the technically more advanced literature on individual manipulation methods. Full references to the original research papers are given throughout, and an up-to-date bibliography is provided for each chapter, which directs the reader to other selected, more specialised sources.