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Quantum Physics: States, Observables and Their Time Evolution (Texts And Monographs In Physics #348)
by Arno Bohm Piotr Kielanowski G. Bruce MainlandThis is an introductory graduate course on quantum mechanics, which is presented in its general form by stressing the operator approach. Representations of the algebra of the harmonic oscillator and of the algebra of angular momentum are determined in chapters 1 and 2 respectively. The algebra of angular momentum is enlarged by adding the position operator so that the algebra can be used to describe rigid and non-rigid rotating molecules. The combination of quantum physical systems using direct-product spaces is discussed in chapter 3. The theory is used to describe a vibrating rotator, and the theoretical predictions are then compared with data for a vibrating and rotating diatomic molecule. The formalism of first- and second-order non-degenerate perturbation theory and first-order degenerate perturbation theory are derived in chapter 4. Time development is described in chapter 5 using either the Schroedinger equation of motion or the Heisenberg’s one. An elementary mathematical tutorial forms a useful appendix for the readers who don’t have prior knowledge of the general mathematical structure of quantum mechanics.
Quantum Physics: The Bottom-Up Approach
by Dirk Dubbers Hans-Jürgen StöckmannThis concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This "quadrature of the circle" is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.
Quantum Physics
by Florian ScheckScheck's Quantum Physics presents a comprehensive introductory treatment, ideally suited for a two-semester course. Part One covers the basic principles and prime applications of quantum mechanics, from the uncertainty relations to many-body systems. Part Two introduces to relativistic quantum field theory and ranges from symmetries in quantum physics to electroweak interactions. Numerous worked-out examples as well as exercises, with solutions or hints, enables the book's use as an accompanying text for courses, and also for independent study. For both parts, the necessary mathematical framework is treated in adequate form and detail. The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory. The new edition was thoroughly revised and now includes new sections on quantization using the path integral method and on deriving generalized path integrals for bosonic and fermionic fields.
Quantum Physics For Dummies
by Andrew Zimmerman JonesThe plain-English guide to understanding quantum physics Mastering quantum physics is no easy feat, but with the help of Quantum Physics For Dummies you can work at your own pace to unlock key concepts and fascinating facts. Packed with invaluable explanations, equations, and step-by-step instructions, this book makes a challenging subject much more accessible. Great for college students taking a quantum physics course, Quantum Physics For Dummies offers complete coverage of the subject, along with numerous examples to help you tackle the tough stuff. The Schrodinger Equation, the foundations of quantum physics, vector notation, scattering theory, angular momentum—it’s all in here. This handy guide helps you prepare for exams and succeed at learning quantum physics. Get clear explanations of the core concepts in quantum physics Review the math principles needed for quantum physics equations Learn the latest breakthroughs and research in the field Clarify difficult subjects and equations from your college courseQuantum Physics For Dummies is great a resource for students who need a supplement to the textbook to help them tackle this challenging subject.
Quantum Scaling In Many-body Systems
by Mucio ContinentinoThis book on quantum phase transitions has been written by one of the pioneers in the application of scaling ideas to many-body systems OCo a new and exciting subject that has relevance to many areas of condensed matter and theoretical physics. One of the few books on the subject, it emphasizes strongly correlated electronic systems. Although dealing with complex problems in statistical mechanics, it does not lose sight of the experiments and the actual physical systems which motivate the theoretical work. The book starts by presenting the scaling theory of quantum critical phenomena. Critical exponents for different systems are calculated using both the momentum space and real space renormalization group approaches. The former is developed without the use of Feynman diagrams, allowing nonspecialists to fully appreciate the underlying physics of this method. The case of heavy fermions as an example of systems close to a zero temperature phase transition is presented and discussed in detail. This is also the case of non-Fermi liquid behavior associated with a quantum critical point. MetalOCoinsulator transitions are discussed within the scaling approach. The book ends with a discussion on first order quantum phase transitions, in particular those which occur due to a fluctuation-induced mechanism. Contents: Scaling Theory of Quantum Critical Phenomena; Landau and Gaussian Theories; Renormalization Group: The A-Expansion; Quantum Phase Transitions; Real Space Renormalization Group Approach; Heavy Fermions; A Microscopic Model for Heavy Fermions; MetalOCoInsulator Transitions; Density-Driven MetalOCoInsulator Transitions; Mott Transitions; The Nonlinear Sigma Model; Fluctuation-Induced Quantum Phase Transitions. Readership: Graduate students, lecturers and researchers in condensed matter physics. "
Quantum Simulations of Materials and Biological Systems
by Jun Zeng Rui-Qin Zhang Herbert TreutleinQuantum Simulations of Materials and Biological Systems features contributions from leading world experts in the fields of density functional theory (DFT) and its applications to material and biological systems. The recent developments of correlation functionals, implementations of Time-dependent algorithm into DFTB+ method are presented. The applications of DFT method to large materials and biological systems such as understanding of optical and electronic properties of nanoparticles, X-ray structure refinement of proteins, the catalytic process of enzymes and photochemistry of phytochromes are detailed. In addition, the book reviews the recent developments of methods for protein design and engineering, as well as ligand-based drug design. Some insightful information about the 2011 International Symposium on Computational Sciences is also provided. Quantum Simulations of Materials and Biological Systems is aimed at faculties and researchers in the fields of computational physics, chemistry and biology, as well as at the biotech and pharmaceutical industries.
Quantum Statistics of Dense Gases and Nonideal Plasmas
by Werner Ebeling Vladimir E. Fortov Vladimir FilinovThe aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter - ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike.
Quantum Theory and Local Causality (SpringerBriefs in Philosophy)
by Péter Vecsernyés Gábor Hofer-SzabóThis book summarizes the results of research the authors have pursued in the past years on the problem of implementing Bell's notion of local causality in local physical theories and relating it to other important concepts and principles in the foundations of physics such as the Common Cause Principle, Bell's inequalities, the EPR (Einstein-Podolsky-Rosen) scenario, and various other locality and causality concepts. The book is intended for philosophers of science with an interest in the formal background of sciences, philosophers of physics and physicists working in foundation of physics.
Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada (CRM Series in Mathematical Physics)
by Pavel Winternitz M. B. Paranjape Richard MacKenzie Zora Thomova William Witczak-KrempaThis volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions.
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2: QTS-X/LT-XII, Varna, Bulgaria, June 2017 (Springer Proceedings in Mathematics & Statistics #255)
by Vladimir DobrevThis book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria.The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists.In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.
Quantum Theory for Mathematicians
by Brian C. HallAlthough ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone-von Neumann Theorem; the Wentzel-Kramers-Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Quantum Tools for Macroscopic Systems (Synthesis Lectures on Mathematics & Statistics)
by Fabio Bagarello Francesco Gargano Francesco OliveriThis book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociology and decision-making. Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a wide range of macroscopic systems both within and outside physics. The mathematical basis of these models is covered in detail, providing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. The authors present an essential resource for researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to complex systems in the social, biological or ecological sciences.Describes how complex systems from a variety of fields can be modeled using quantum mechanical ideasProvides insight into the dynamics of macroscopic systems and opens new interdisciplinary research frontiersIntroduces quantum tools needed for the analysis of the dynamical behavior of macroscopic systems
Quantum Transport
by Yuli V. Nazarov Yaroslav M. BlanterQuantum transport is a diverse field, sometimes combining seemingly contradicting concepts - quantum and classical, conduction and insulating - within a single nanodevice. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the nanoscale. This textbook, first published in 2009, is a comprehensive introduction to the rapidly developing field of quantum transport. The authors present the comprehensive theoretical background, and explore the groundbreaking experiments that laid the foundations of the field. Ideal for graduate students, each section contains control questions and exercises to check readers' understanding of the topics covered. Its broad scope and in-depth analysis of selected topics will appeal to researchers and professionals working in nanoscience.
Quantum Transport in Interacting Nanojunctions: A Density Matrix Approach (Lecture Notes in Physics #1024)
by Andrea Donarini Milena GrifoniThis book serves as an introduction to the growing field of quantum many-body transport in interacting nanojunctions. It delves into a theoretical approach based on a general density-matrix formulation for open quantum systems. In the book, relevant transport observables, like the current or its higher order cumulants, are obtained by evaluating quantum statistical averages. This approach requires the knowledge of the reduced density matrix of the interacting nanosystems. The formulation for addressing transport problems, based on the evolution of the reduced density operator in Liouville space, is highly versatile. It enables the treatment of charge and spin transport across various realistic nanostructures. Topics encompass standard Coulomb blockade, cotunneling phenomena in quantum dots, vibrational and Franck-Condon effects in molecular junctions, as well as many-body interference observed in double quantum dots or carbon nanotubes. Derived from lectures tailored for graduate and advanced students at the University of Regensburg in Germany, this book is enriched with exercises and step-by-step derivations.
Quantum Triangulations
by Annalisa Marzuoli Mauro CarforaResearch on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Quantum versus Classical Mechanics and Integrability Problems: towards a unification of approaches and tools
by Maciej BłaszakThis accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Quartz: Deposits, Mineralogy and Analytics
by Jens Götze Robert MöckelThe book will include contributions of the state of the art of quartz raw materials (deposits and properties) and their analytics. The chapters are presented by leading scientists in the quartz field. The presentations cover the main interrelations between genesis of quartz - formation of specific properties - analytics - industrial applications of SiO2 raw materials.
Quartz: Deposits, Mineralogy and Analytics (Springer Geology)
by Jens Götze Robert MöckelThe book will include contributions of the state of the art of quartz raw materials (deposits and properties) and their analytics. The chapters are presented by leading scientists in the quartz field. The presentations cover the main interrelations between genesis of quartz - formation of specific properties - analytics - industrial applications of SiO2 raw materials.
Quasi-Exactly Solvable Models in Quantum Mechanics
by A.G UshveridzeExactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward.Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics.Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.
Quasi-Geostrophic Theory of Oceans and Atmosphere
by Fabio Cavallini Fulvio CriscianiLarge-scale winds and currents tend to balance Coriolis and pressure gradient forces. The time evolution of these winds and currents is the subject of the quasi-geostrophic theory. Chapter 1 presents concepts and equations of classical inertial fluid mechanics. Chapter 2 deals with the equations of thermodynamics that close the governing equations of the fluids. Then, the motion is reformulated in a uniformly rotating reference frame. Chapter 3 deals with the shallow-water model and the homogeneous model of wind-driven circulation. The chapter also describes a classical application of the Ekman layer to the atmosphere. Chapter 4 considers the two-layer model, as an introduction to baroclinic flows, together with the concept of available potential energy. Chapter 5 takes into account continuously stratified flows in the ocean and in the atmosphere.
Quasi-linear Theory for Surface Wave-Current Interactions (Mathematics of Planet Earth)
by James C. McWilliamsThis book introduces a mathematical theory for the interaction of oceanic surface gravity waves and oceanic currents. This theory is formulated using the quasi-linear approximation for a uniform density fluid with a free surface and it provides wave-averaged expressions for the wave amplitudes and for the dynamical evolution of the currents. The surface gravity wave–current interaction theory is a more complete theory than previous with respect to an asymptotic expansion in the small parameter V/C, where V is a current speed and C is a wave speed. This book also illustrates the formal theory with several examples, and the path for its implementation in more realistic wave and circulation models is envisioned. This book is appealing to oceanic research scientists and mathematicians interested in geophysical fluid dynamics.
Quaternary Carbonate and Evaporite Sedimentary Facies and Their Ancient Analogues: A Tribute to Douglas James Shearman (International Association Of Sedimentologists Ser. #106)
by Christopher G. St.C. Kendall Abdulrahman S. Alsharhan Ian Jarvis Tom StevensThis book is part of the International Association of Sedimentologists (IAS) Special Publications. The Special Publications from the IAS are a set of thematic volumes edited by specialists on subjects of central interest to sedimentologists. Papers are reviewed and printed to the same high standards as those published in the journal Sedimentology and several of these volumes have become standard works of reference. This volume commemorates the eclectic research of Douglas James Shearman into evaporites, which was initiated by his studies of the prograding UAE coastal sabkhas or salt flats that incorporate evaporite minerals which displace and replace earlier carbonate sediments. His subsequent proselytization of the study of ancient evaporites in sedimentary sections all over the world led to fundamental advances in our understanding of arid zone carbonate sedimentology. The papers presented here are based on presentations made in Abu Dhabi, UAE 12-14th October 2004 and 7th –8th November 2006. They provide a retrospective from the 1960's and 70's of Holocene evaporites and carbonates, recapturing Shearman's contribution by revisiting the Holocene coastal evaporite and carbonate sediments of the Arabian/Persian Gulf from Abu Dhabi, Qatar, and Oman. The first set of papers considers these sediments from the perspective of their coastal geomorphology, sedimentary character and their geochemistry. Later papers examine the significance of these settings in the ancient geological section world-wide, including examples from the Mesozoic-Cenozoic of the Moroccan Atlantic margin and the Upper Jurassic Arab Formation of the Arabian Gulf.
Quaternary Climate Change over the Indian Subcontinent
by Neloy KhareQuaternary studies provide the essential context for evaluation of what is happening with the earth's climate today, and to clarify our vulnerability to hazardous natural processes. This book covers scientific aspects of past and present climatic changes of the quaternary period focused on the Indian subcontinent via response of modern environmental conditions on climate proxies, reconstruction of paleoclimate, paleomonsoon, glacial geology, climate variabilities using dendrochronology, cave deposits including quaternary tectonics and climate change over the Himalayan region. It consists of data generated from different landforms including lakes, caves, rivers, swamps, pits, and trenches using different proxies. Aimed at researchers, graduate students, professionals in geology, geography and environmental sciences, micropaleontology, and Quaternary climate change, this book: Studies Quaternary climate using various proxies in varied environments on the Indian sub-continent Covers pertinent historical and environmental archives to understand the current climate scenario Discusses the impact of climate change on biotic and abiotic components Includes thorough review of paleoclimate change studies Devotes significant space to glacial geology and all glacial climate proxies
Quaternary Dating Methods
by Mike WalkerThis introductory textbook introduces the basics of dating, the range of techniques available and the strengths and limitations of each of the principal methods.Coverage includes:the concept of time in Quaternary Science and related fieldsthe history of dating from lithostratigraphy and biostratigraphythe development and application of radiometric methodsdifferent methods in dating: radiometric dating, incremental dating, relative dating and age equivalencePresented in a clear and straightforward manner with the minimum of technical detail, this text is a great introduction for both students and practitioners in the Earth, Environmental and Archaeological Sciences.Praise from the reviews:"This book is a must for any Quaternary scientist." SOUTH AFRICAN GEOGRAPHICAL JOURNAL, September 2006"...very well organized, clearly and straightforwardly written and provides a good overview on the wide field of Quaternary dating methods..." JOURNAL OF QUATERNARY SCIENCE, January 2007
Quaternary Deserts and Climatic Change
by K. W. Glennie A. S. Alsharhan G. L. Whittle C.G. St.C. KENDALLThese proceedings record the results of climate change in many areas which are hyper-arid deserts today but which, almost cyclically, at intervals of thousands or even hundreds of thousands of years, have had a much more humid climate.