Quantum Mechanics For Physicists

This book explores the nature of quantum entanglement and quantum information and their role in the quantum world. Their relations to a number of key experiments and thought experiments in the history of quantum physics are considered, as is a range of interpretations of quantum mechanics that have been put forward as a means of understanding the fundamental nature of microphysics - the traditionally accepted domain of quantum mechanics - and in some cases, the universe as a whole. In this way, the book reveals the deep significance of entanglement and quantum information for our understanding of the physical world.

The focus of the present work is nonrelativistic and relativistic quantum mechanics with standard applications to the hydrogen atom. The author has aimed at presenting quantum mechanics in a comprehensive yet accessible for mathematicians and other non-physicists. The genesis of quantum mechanics, its applications to basic quantum phenomena, and detailed explanations of the corresponding mathematical methods are presented. The exposition is formalized (whenever possible) on the basis of the coupled Schroedinger, Dirac and Maxwell equations. Aimed at upper graduate and graduate students in mathematical and physical science studies.

This book offers a history of the instrumentation used to materialize the early thought experiments devised in the Einstein-Bohr disputes over the foundations of quantum mechanics. It shows how the second world war and cold war fostered the development of materials, instruments, and systems that made it possible to create, manipulate, and detect single quantum systems, thus creating the material conditions for experiments in foundations of quantum mechanics and for a broad spectrum of experimental inquiries on the structure and properties of matter which underlay the creation of new research fields such as quantum optics, quantum information, and atomic, molecular, and optical physics. Discussing research and development performed in diverse contexts, this book reveals how physicists carried instruments, and the knowledge they embodied, through disciplinary and geographic frontiers to probe entanglement, a most intriguing feature of the quantum world.

Quantum mechanics and quantum field theory are highly successful physical theo­ ries that have numerous practical applications. Largely mathematical in character, these theories continue to stimulate the imaginations of applied mathematicians and purists as weIl. In recent years, in particular, as a new array of tools have emerged, including a representative amount from the domain of so-called pure mathematics, interest in both the conceptual and physical aspects of these beau­ tiful subjects has especially blossomed. Given the emergence of newer and of­ ten spectacular applications of mathematics to quantum theory, and to theoretical physics in general, one notes that certain communication gaps between physicists and mathematicians continue to be bridged. This text on quantum mechanics, designed primarily for mathematics students and researchers, is an attempt to bridge further gaps. Although the mathematical style presented is generally precise, it is counterbalanced at some points by a re­ laxation of precision, as our overall purpose is to capture the basic fiavor of the subject both formally and intuitively. The approach is one in which we attempt to maintain sensitivity with respect to diverse backgrounds of the readers, including those with modest backgrounds in physics. Thus we have included several con­ crete computational examples to fortify stated principles, several appendices, and certain basic physical concepts that help to provide for a reasonably self-contained account of the material, especially in the first 11 chapters.