John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.

A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

This book is the most complete collection of John S Bell's research papers, review articles and lecture notes on the foundations of quantum mechanics. Some of this material has hitherto been difficult to access. The book also appears in a paperback edition, aimed at students and young researchers.This volume will be very useful to researchers in the foundations and applications of quantum mechanics.

After a quarter century of discoveries that rattled the foundations of classical mechanics and electrodynamics, the year 1926 saw the publication of two works intended to provide a theoretical structure to support new quantum explanations of the subatomic world. Heisenberg's matrix mechanics and Schrodinger’s wave mechanics provided compatible but mathematically disparate ways of unifying the discoveries of Planck, Einstein, Bohr and many others. Efforts began immediately to prove the equivalence of these two structures, culminated successfully by John von Neumann’s 1932 volume "Mathematical Foundations of Quantum Mechanics." This forms the springboard for the current effort. We begin with a presentation of a minimal set of von Neumann postulates while introducing language and notation to facilitate subsequent discussion of quantum calculations based in finite dimensional Hilbert spaces. Chapters which follow address two-state quantum systems (with spin one-half as the primary example), entanglement of multiple two-state systems, quantum angular momentum theory and quantum approaches to statistical mechanics. A concluding chapter gives an overview of issues associated with quantum mechanics in continuous infinite-dimensional Hilbert spaces.

Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.

Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.