Quantum states of atoms and molecules The translational symmetry and quantum states in periodic and amorphous solids Band structure and tuning Classical and quantum statistics with applications to ideal gases (photons, phonons and electrons, molecules) Quantum states in type-I and type-II superconductors (elementary theory included) Magnetic materials, materials with GMR and CMR Shape memory effects in alloys and materials 2D materials (graphene and graphene analogus) NLO and photovoltaic materials Hydrogen storage material for mitigating the looming energy crisis Quantum states in low and high band gap semiconductors Semimetals Designer materials, etc.

Magnetic and spintronic materials are ubiquitous in modern technological applications, e.g. in electric motors, power generators, sensors and actuators, not to mention information storage and processing. Medical technology has also greatly benefited from magnetic materials - especially magnetic nanoparticles - for therapy and diagnostics methods. All of the above-mentioned applications rely on the properties of the materials used. These properties in turn depend on intrinsic and extrinsic material parameters. The former are related to the actual elements used and their properties, e.g. atomic magnetic moment and exchange interaction between atoms; the latter are related to the structural and microstructural properties of the materials used, e.g. their crystal structure, grain size, and grain boundary phases. Focusing on state-of-the-art magnetic and spintronic materials, this book will introduce readers to a range of related topics in Physics and Materials Science. Phenomena and processes at the nanoscale are of particular importance in this context; accordingly, much of the book addresses such topics.

Based on the analytical methods and the computer programs presented in this book, all that may be needed to perform MRI tissue diagnosis is the availability of relaxometric data and simple computer program proficiency. These programs are easy to use, highly interactive and the data processing is fast and unambiguous. Laboratories (with or without sophisticated facilities) can perform computational magnetic resonance diagnosis with only T1 and T2 relaxation data. The results have motivated the use of data to produce data-driven predictions required for machine learning, artificial intelligence (AI) and deep learning for multidisciplinary and interdisciplinary research. Consequently, this book is intended to be very useful for students, scientists, engineers, the medical personnel and researchers who are interested in developing new concepts for deeper appreciation of computational magnetic resonance imaging for medical diagnosis, prognosis, therapy and management of tissue diseases.

In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics appear as special cases. They are the sources of familiar names such as "orbital angular momentum," "spin-orbit coupling" and "magnetic moment" for operators of the relativistic quantum formalism. The theory of binaries, in terms of differential equations, is treated for the first time in this book. These have the mathematical structure of the corresponding one-body equations (Klein-Gordon for two spinless particles, Dirac for two spinor particles) with a relativistically reduced mass. They allow the calculation of radiative corrections via the vector potential operator. This second edition of the successful textbook adds various new sections on relativistic quantum chemistry and on the relativistic treatment of the proton in hydrogen. Others chapters have been expanded, e.g. on hyperfinite interactions, or carefully revisited.

Quantum mechanics is one of mankind's most remarkable intellectual achievements. Stunningly successful and elegant, it challenges our deepest intuitions about the world. In this book, seventeen physicists and philosophers, all deeply concerned with understanding quantum mechanics, reply to Schlosshauer's penetrating questions about the central issues. They grant us an intimate look at their radically different ways of making sense of the theory's strangeness. What is quantum mechanics about? What is it telling us about nature? Can quantum information or new experiments help lift the fog? And where are we headed next? Everyone interested in the contemporary but often longstanding conundrums of quantum theory, whether lay reader or expert, will find much food for thought in these pages. A wealth of personal reflections and anecdotes guarantee an engaging read. Participants: Guido Bacciagaluppi, Caslav Brukner, Jeffrey Bub, Arthur Fine, Christopher Fuchs, GianCarlo Ghirardi, Shelly Goldstein, Daniel Greenberger, Lucien Hardy, Anthony Leggett, Tim Maudlin, David Mermin, Lee Smolin, Antony Valentini, David Wallace, Anton Zeilinger, and Wojciech Zurek.

This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere.This book - originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 - dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source.

This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.

Based on the lectures given at TU Munich for third-year physics students, this book provides the basic concepts of relativistic quantum field theory, perturbation theory, Feynman graphs, Abelian and non-Abelian gauge theories, with application to QED, QCD, and the electroweak Standard Model. It also introduces quantum field theory and particle physics for beginning graduate students with an orientation towards particle physics and its theoretical foundations. Phenomenology of W and Z bosons, as well as Higgs bosons, is part of the electroweak chapter in addition to recent experimental results, precision tests and current status of the Standard Model.

The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.A third published text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schroedinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage. The current book provides the solutions to those problems.The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.

With contributions by leading theoreticians, this book presents the discoveries of hitherto hidden connections between seemingly unrelated fields of fundamental physics. The topics range from cosmology and astrophysics to nuclear-, particle- and heavy-ion science. A current example concerns the sensitivity of gravitational wave spectra to the phase structure of dense nuclear and quark matter in binary neutron star collisions. The contributions by Hanauske and Stoecker as well as Banik and Bandyopadhyay relate the consequent insights to hot dense nuclear matter created in supernova explosions and in high-energy heavy-ion collisions. Studies of the equation of state for neutron stars are also presented, as are those for nuclear matter in high-energy heavy-ion collisions. Other reviews focus on QCD-thermodynamics, charmed mesons in the quark-gluon plasma, nuclear theory, extensions to the standard general theory of relativity, new experimental developments in heavy ion collisions and renewable energy networks. The book will appeal to advanced students and researchers seeking a broad view of current challenges in theoretical physics and their interconnections.

This work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader 's disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches.

This introduction to quantum field theory (QFT) is written by a physical chemist for physical chemists, chemical physicists, and other non-physicists with knowledge of quantum theory but who want to explore ways in which they might use the power of QFT in their investigations. This book starts where many graduate courses in quantum theory that are offered to chemistry students leave off and first develops some of the necessary tools, such as Fock algebra, which is applied to solving the quantum oscillator problem. Then it is used to develop the theory of coherent states, time-dependent perturbation theory, and the treatment of bosons and fermions. With this background, the QFT of a perfect gas is derived and a connection to thermodynamics is demonstrated. Application to imperfect gases provides a new approach to modelling gas-liquid phase transitions. The book concludes with photons and their interaction with molecular ensembles, and brings us to full circle by deriving the blackbody radiation law, which started it all. The power of the QFT methodology and the breadth of its applications should fascinate the reader as it has the author.

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner ..". if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.

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 standard physics textbooks - which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles.

Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field.

This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.

This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein-Dirac equations, nonlinear Heisenberg's spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.