The book considers foundational thinking in quantum theory, focusing on the role the fundamental principles and principle thinking there, including thinking that leads to the invention of new principles, which is, the book contends, one of the ultimate achievements of theoretical thinking in physics and beyond. The focus on principles, prominent during the rise and in the immediate aftermath of quantum theory, has been uncommon in more recent discussions and debates concerning it. The book argues, however, that exploring the fundamental principles and principle thinking is exceptionally helpful in addressing the key issues at stake in quantum foundations and the seemingly interminable debates concerning them. Principle thinking led to major breakthroughs throughout the history of quantum theory, beginning with the old quantum theory and quantum mechanics, the first definitive quantum theory, which it remains within its proper (nonrelativistic) scope. It has, the book also argues, been equally important in quantum field theory, which has been the frontier of quantum theory for quite a while now, and more recently, in quantum information theory, where principle thinking was given new prominence. The approach allows the book to develop a new understanding of both the history and philosophy of quantum theory, from Planck’s quantum to the Higgs boson, and beyond, and of the thinking the key founding figures, such as Einstein, Bohr, Heisenberg, Schrödinger, and Dirac, as well as some among more recent theorists. The book also extensively considers the nature of quantum probability, and contains a new interpretation of quantum mechanics, “the statistical Copenhagen interpretation.” Overall, the book’s argument is guided by what Heisenberg called “the spirit of Copenhagen,” which is defined by three great divorces from the preceding foundational thinking in physics—reality from realism, probability from causality, and locality from relativity—and defined the fundamental principles of quantum theory accordingly.

This text presents a rigorous mathematical account of the principles of quantum mechanics, in particular as applied to chemistry and chemical physics. Applications are used as illustrations of the basic theory. The first two chapters serve as an introduction to quantum theory, although it is assumed that the reader has been exposed to elementary quantum mechanics as part of an undergraduate physical chemistry or atomic physics course. Following a discussion of wave motion leading to Schrödinger's wave mechanics, the postulates of quantum mechanics are presented along with essential mathematical concepts and techniques. The postulates are rigorously applied to the harmonic oscillator, angular momentum, the hydrogen atom, the variation method, perturbation theory, and nuclear motion. Modern theoretical concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder operators are introduced and used throughout. This text is appropriate for beginning graduate students in chemistry, chemical physics, molecular physics and materials science.

The second edition of this book deals, as the first, with the foundations of classical physics from the 'symplectic' point of view, and of quantum mechanics from the 'metaplectic' point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the 'principle of the symplectic camel', which is a deep topological property of Hamiltonian flows. We introduce the notion of 'quantum blob', which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the 'metatron' is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

Quantum Physics for Scientists and Technologists is a self-contained, comprehensive review of this complex branch of science. The book demystifies difficult concepts and views the subject through non-physics fields such as computer science, biology, chemistry, and nanotechnology. It explains key concepts and phenomena in the language of non-physics majors and with simple math, assuming no prior knowledge of the topic. This cohesive book begins with the wavefunction to develop the basic principles of quantum mechanics such as the uncertainty principle and wave-particle duality. Comprehensive coverage of quantum theory is presented, supported by experimental results and explained through applications and examples without the use of abstract and complex mathematical tools or formalisms. From there, the book: Takes the mystery out of the Schrodinger equation, the fundamental equation of quantum physics, by applying it to atoms Shows how quantum mechanics explains the periodic table of elements Introduces the quantum mechanical concept of spin and spin quantum number, along with Pauli's Exclusion Principle regarding the occupation of quantum states Addresses quantum states of molecules in terms of rotation and vibration of diatomic molecules Explores the interface between classical statistical mechanics and quantum statistical mechanics Discusses quantum mechanics as a common thread through different fields of nanoscience and nanotechnology Each chapter features real-world applications of one or more quantum mechanics principles. "Study Checkpoints" and problems with solutions are presented throughout to make difficult concepts easy to understand. In addition, pictures, tables, and diagrams with full explanations are used to present data and further explain difficult concepts. This book is designed as a complete course in quantum mechanics for senior undergraduates and first-year graduate students in non-physics majors. It also applies to courses such as modern physics, physical chemistry and nanotechnology. The material is also accessible to scientists, engineers, and technologists working in the fields of computer science, biology, chemistry, engineering, and nanotechnology.

R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

This comprehensive volume gives a balanced and systematic treatment of both the interpretation and the mathematical-conceptual foundations of quantum mechanics. It is written in a pedagogical style and addresses many thorny problems of fundamental physics. The first aspect concerns Interpretation. The author raises the central problems: formalism, measurement, non-locality, and causality. The main positions on these subjects are presented and critically analysed. The aim is to show that the main schools can converge on a core interpretation. The second aspect concerns Foundations. Here it is shown that the whole theory can be grounded on information theory. The distinction between information and signal leads us to integrating quantum mechanics and relativity. Category theory is presented and its significance for quantum information shown; the logic and epistemological bases of the theory are assessed. Of relevance to all physicists and philosophers with an interest in quantum theory and its foundations, this book is destined to become a classic work.

Quantum Mechanics II: Advanced Topics offers a comprehensive exploration of the state-of-the-art in various advanced topics of current research interest. A follow-up to the authors’ introductory book Quantum Mechanics I: The Fundamentals, this book expounds basic principles, theoretical treatment, case studies, worked-out examples and applications of advanced topics including quantum technologies. A thoroughly revised and updated this unique volume presents an in-depth and up-to-date progress on the growing topics including latest achievements on quantum technology. In the second edition six new chapters are included and the other ten chapters are extensively revised. Features Covers classical and quantum field theories, path integral formalism and supersymmetric quantum mechanics. Highlights coherent and squeezed states, Berry’s phase, Aharonov—Bohm effect and Wigner function. Explores salient features of quantum entanglement and quantum cryptography. Presents basic concepts of quantum computers and the features of no-cloning theorem and quantum cloning machines. Describes the theory and techniques of quantum tomography, quantum simulation and quantum error correction. Introduces other novel topics including quantum versions of theory of gravity, cosmology, Zeno effect, teleportation, games, chaos and steering. Outlines the quantum technologies of ghost imaging, detection of weak amplitudes and displacements, lithography, metrology, teleportation of optical images, sensors, batteries and internet. Contains several worked-out problems and exercises in each chapter. Quantum Mechanics II: Advanced Topics addresses various currently emerging exciting topics of quantum mechanics. It emphasizes the fundamentals behind the latest cutting-edge developments to help explain the motivation for deeper exploration. The book is a valuable resource for graduate students in physics and engineering wishing to pursue research in quantum mechanics.

Quantum mechanics touches all areas of physics, chemistry, life sciences, and engineering. It has emerged as a tool for researching and developing new technology that has had a deep impact on modern life. An essential ingredient of quantum mechanics is the role of the observer and the duality between particle and wave properties of matter at very small scales. This book covers such topics as complex space forms of quantum mechanics, entropy in quantum mechanics, and equations of relativistic quantum mechanics as well as applications of quantum mechanics to more complicated situations. Written by international experts, the book illustrates the wide scope, influence, and applicability of quantum mechanics.

Comprehensive survey of quantum theory and its formalism demonstrates establishment of specific pairs of conjugate observables and the determination of their properties. Also relies on the Dirac equation and explains spin-statistics theorem. 2020 edition.