Mathematical Structures of Quantum Mechanics

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.

This original 2018 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students

This book is a comprehensive text in the field of quantum mechanics, covering fundamental concepts including the state of a quantum mechanical system, operators, superposition principle and measurement postulate. The notion of an operator and the algebra of operators are introduced with the help of elementary concepts of mathematical analysis. Mathematical tools developed will help readers in understanding the difficulties encountered in classical physics while trying to explain the experimental results involving atomic spectra and other phenomena. The differential equations that arise while solving eigenvalue problems are solved rigorously, to make the text self-sufficient. The solutions are then physically interpreted and explained. The text offers solved examples, analogous and homework problems to help students in solving practical problems of physics requiring quantum mechanical treatment.

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Founda

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Founda

The important changes quantum mechanics has undergone in recent years are reflected in this approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with developments in the field. Historical, mathematical and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available a

The second edition of Elementary Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This readable book teaches in d

At a level accessible to advanced undergraduates, this textbook explains the fundamental role of quantum mechanics in determining the structure, dynamics, and other properties of molecules. Readers wi

This marvelous book is aimed at strengthening the mathematical background and sharpening the mathematical tools of students without rigorous training before taking the quantum mechanics course. The ab

Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.

The important changes quantum mechanics has undergone in recent years are reflected in this approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with developments in the field. Historical, mathematical and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available a

Rather than concentrating on the needs of physicists, Lawden (University of Aston) wrote for undergraduate and graduate students of applied mathematics. In this reproduction of the 1967 edition publis

Written for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on careful formulation rather than problem-solving. All physical concept

Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth cent

Reviews from the First Edition:"An excellent text ??Y The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)"No matter

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arn

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary

Introductory text provides foundation in the mathematical study and properties of wave motion. Topics include physical consequences of wave theory of material properties and extensive applications to

This book represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to speci

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

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Strocchi (Scuola Normale Superiore, Italy) delivered the lecture series from 1993 to 1996 as a half-semester course for undergraduate mathematics students. Classical mechanics tend to be part of a sta

This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from

Four concise, brilliant lectures on mathematical methods in quantum mechanics from Nobel Prize-winning quantum pioneer build on idea of visualizing quantum theory through the use of classical mechani

Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throu

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced

The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrodinger and rando

This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in st

Gallone presents students, academics, and researchers with an investigation of the mathematical foundations and theory of non-relativistic quantum mechanics. The author has organized the main body of

Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at thi

Originally published in 1981, this book forms volume 15 of the Encyclopedia of Mathematics and its Applications. The text provides a clear and thorough treatment of its subject, adhering to a clean exposition of the mathematical content of serious formulations of rational physical alternatives of quantum theory as elaborated in the influential works of the period, to which the authors made a significant contribution. The treatment falls into three distinct, logical parts: in the first part, the modern version of accumulated wisdom is presented, avoiding as far as possible the traditional language of classical physics for its interpretational character; in the second part, the individual structural elements for the logical content of the theory are laid out; in part three, the results of section two are used to reconstruct the usual Hilbert space formulation of quantum mechanics in a novel way.

Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.

This classic of modern physics includes a vast array of approximation methods, mathematical tricks, and physical pictures useful in applying quantum mechanics to other fields. Students and professiona

If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than 160 homework problems help students to problem solve and to practise applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schrödinger's equation, operators, and approximation methods. Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information, are also covered. Practical applications and algorithms for the computational analysis of simple structures make this an ideal introduction to quantum mechanics for students of engineering, physics, nan