In this undergraduate textbook, now in its 2nd edition, the author develops the quantum theory from first principles based on very simple experiments: a photon traveling through beam splitters to detectors, an electron moving through magnetic fields, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers. The first part of the book examines how experimental facts force us to let go of some deeply held preconceptions and develops this idea into a description of states, probabilities, observables, and time evolution. The quantum mechanical principles are illustrated using applications such as gravitational wave detection, magnetic resonance imaging, atomic clocks, scanning tunneling microscopy, and many more. The first part concludes with an overview of the complete quantum theory. The second part of the book covers more advanced topics, including the concept of entanglement, the process of decoherence or how quantum systems become classical, quantum computing and quantum communication, and quantum particles moving in space. Here, the book makes contact with more traditional approaches to quantum physics. The remaining chapters delve deeply into the idea of uncertainty relations and explore what the quantum theory says about the nature of reality. The book is an ideal accessible introduction to quantum physics, tested in the classroom, with modern examples and plenty of end-of-chapter exercises.

This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov-Witten invariants of a Calabi-Yau threefold by using the Picard-Fuchs differential equation of period integrals of its mirror Calabi-Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.On the B-model side, the process of construction of a pair of mirror Calabi-Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard-Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.

""The Cosmic Code" can be read by anyone. I heartily recommend it " -- "The""New York Times Book Review
""A reliable guide for the nonmathematical reader across the highest ridges of physical theory. Pagels is unfailingly lighthearted and confident." -- "Scientific American
""A sound, clear, vital work that deserves the attention of anyone who takes an interest in the relationship between material reality and the human mind." -- "Science 82
"This is one of the most important books on quantum mechanics ever written for general readers. Heinz Pagels, an eminent physicist and science writer, discusses and explains the core concepts of physics without resorting to complicated mathematics. The two-part treatment outlines the history of quantum physics and addresses complex subjects such as Bell's theorem and elementary particle physics, drawing upon the work of Bohr, Gell-Mann, and others. Anecdotes from the personal documents of Einstein, Oppenheimer, Bohr, and Planck offer intimate glimpses of the scientists whose work forever changed the world.

This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolas Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.

This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms. The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.

Group Theoretical Foundations of Quantum Mechanics

This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics will find this book to be a valuable treatment of the control of an important class of quantum systems. The material presented here will also interest physicists working in optics, quantum optics, quantum information theory and other quantum-physical disciplines.

As Kenneth W. Ford shows us in "The Quantum World," the laws governing the very small and the very swift defy common sense and stretch our minds to the limit. Drawing on a deep familiarity with the discoveries of the twentieth century, Ford gives an appealing account of quantum physics that will help the serious reader make sense of a science that, for all its successes, remains mysterious. In order to make the book even more suitable for classroom use, the author, assisted by Diane Goldstein, has included a new section of Quantum Questions at the back of the book. A separate answer manual to these 300+ questions is available; visit "The Quantum World" website for ordering information.

There is also a cloth edition of this book, which does not include the "Quantum Questions" included in this paperback edition.

Statistical Mechanics, Fourth Edition, explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. This valuable textbook introduces the reader to the historical context of the subject before delving deeper into chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. In the latest revision, the book's authors have updated the content throughout, including new coverage on biophysical applications, updated exercises, and computer simulations. This updated edition will be an indispensable to students and researchers of statistical mechanics, thermodynamics, and physics.

Three studies address current theoretical problems in quantum nonstationary oscillators that use Wigner representation and supersymmetries. They discuss fundamental aspects of quantum field theory and applications of oscillator models in optics and electromagnetic fields and radiation. Translated from the Russian. Acidic paper. Annotation copyright

In this classic treatise, presenting a complete physical picture of quantum theory, Nobel laureate Heisenberg covers not only his own far-reaching contributions to quantum theory, but also those of Dirac, Schroedinger, Compton, Wilson, Einstein and others. "An authoritative statement of Heisenberg's views on this aspect of the quantum theory" - Nature.

The spellbinding stories of the scientists whose eureka! breakthroughs in modern physics reveal science's astonishing predictive power. 'An excellent popular science book.' DARA O BRIAIN 'A thoroughly informative and entertaining read.' ANNA BURNS, Booker Prize-winning author of Milkman 'One of the best-written books about phsyics I have ever come across.' POPULAR SCIENCE 'Highly entertaining and accessible.' IRISH TIMES 'Fascinating, life enhancing entertainment.' PROSPECT 'Thoroughly enjoyable . . . Chown has done it again.' BBC SKY AT NIGHT Breakthrough takes us on a breathtaking, mind-altering tour of the eureka! moments of modern physics. Charting the spellbinding stories of the scientists who predicted and discovered the existence of unknown planets, black holes, invisible force fields, ripples in the fabric of space-time, unsuspected subatomic particles and even antimatter, Marcus Chown reveals science's greatest mystery: its astonishing predictive power. *** Breakthrough was previously published in 2020 in hardback under the title The Magicians.

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom-Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson-Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quantum field theorists, and probabilists, including graduate and advanced undergraduate students.

This volume presents the peer-reviewed proceedings of the XXIII DAE-BRNS High Energy Physics Symposium 2018, which was held at the Indian Institute of Technology Madras, India, on 10-15 December 2018. Gathering selected contributions, the book highlights the latest developments and research trends in physics, detectors and instrumentation relevant to all branches of particle physics, astroparticle physics and closely related fields. The major topics covered include Standard Model physics, beyond Standard Model physics, neutrino physics, cosmology, formal theory, heavy ion physics & quantum chromodynamics (QCD), particle detectors and future experiments. Given the range of topics discussed, the book will be useful for beginners as well as advanced researchers in the field.

The book discusses the recent experimental results obtained at the LHC that involve electroweak bosons. The results are placed into an appropriate theoretical and historical context. The work pays special attention to the rising subject of hadronically decaying bosons with high boosts, documenting the state-of-the-art identification techniques and highlighting typical results. The text is not limited to electroweak physics in the strict sense, but also discusses the use of electroweak vector-bosons as tool in the study of other subjects in particle physics, such as determinations of the proton structure or the search for new exotic particles. The book is particularly well suited for graduate students, starting their thesis work on topics that involve electroweak bosons, as the book provides a comprehensive description of phenomena observable at current accelerators as well as a summary of the most relevant experimental techniques.

Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to various effective models of chiral symmetry breaking in strong interactions and the BEH-mechanism of symmetry breaking in the electroweak theory. After introducing the basics of the functional integral formulation of quantum field theories and the derivation of different variants of the equations which determine the n-point functions, the text elaborates on the formulation of the optimized perturbation theory and the large-N expansion, as applied to the solution of these underlying equations in vacuum. The optimisation aspects of the 2PI approximation is discussed. Each of them is presented as a specific reorganisation of the weak coupling perturbation theory. The dimensional reduction of high temperature field theories is discussed from the same viewpoint. The renormalization program is described for each approach in detail and particular attention is paid to the appropriate interpretation of the notion of renormalization in the presence of the Landau singularity. Finally, results which emerge from the application of these techniques to the thermodynamics of strong and electroweak interactions are reviewed in detail.

This volume presents results from fundamental research on the phenomenon of phase conjugation of laser emission discovered at the Physics Institute of the Academy of Sciences during stimulated scattering in hypersound, and with four-wave interaction in a wavelength range from the visible through the mid-infrared. Fundamentally new optical designs and methods of controlling laser emission are proposed and tested experimentally on the basis of this effect.

"Semiclassical Physics" explores the fascinating and deep connection between classical motion and quantum fluctuations. The book conveys a way of describing quantum effects in a physical system using the periodic orbit theory of Gutzwiller, which focuses on the classical dynamics of the system. The authors seek to demonstrate its usefulness for understanding quantum fluctuations in interacting many-body systems, exhibiting the close link of the shorter classical periodic orbits with the partly resolved shell fluctuations. The extended Thomas-Fermi model is developed in detail and shown to describe the average properties of finite fermion systems in a self-consistent mean-field approach. The new, updated paperback edition includes: Basic introduction to semiclassical physics for the general reader Elementary derivation of the Gutzwiller trace formula for chaotic systems; thorough discussion of its extensions to mixed and integrable systems, uniform approximations, and diffractive corrections Unified presentation of extended Thomas-Fermi model, Wigner-Kirkwood expansion, Weyl and Euler-MacLaurin expansions, and Strutinsky averaging Relations of the Gutzwiller theory to the Selberg trace formula and Bogomolny's transfer-matrix method Applications to finite fermion systems in nuclear, atomic and condensed matter physics Analytical examples and educational problems with hints to their solution Appendices to facilitate further detailed study The book addresses graduate students with a basic knowledge of classical and quantum mechanics and scientists with an interest in semiclassical methods. The approach is informal, guided largely by simple solvable models and by practical applications toreal physical phenomena.

This book highlights the recent research works on computer science, electrical and electronic engineering which was presented virtually during the 2nd International Conference on Computer Science, Electrical & Electronic Engineering (ICCEE 2020) on 17th and 18th August 2020. Written by leading researchers and industry professionals, the papers highlight recent advances and address current issues in the respective fields.

Unlike many textbooks or popular science books, A Simple Guide to Popular Physics has truly been crafted for the uninitiated or those spooked by the subject's complexity. Harris's inviting guide promises to give "absolute beginners" from "teens to centenarians" a basic grounding in particle physics, quantum physics, and cosmology-all without making readers do math. With the goal of introducing the basics and encouraging readers to explore more deeply afterwards, Harris notes "Like the fish we have no notion of what is beyond the boundaries of our knowledge, but unlike the fish, we know there is something." He starts by presenting those boundaries, the fundamentals of classic physics (Newton's law, states of matter, types of energy), with crisp clarity before laying out an accessible explanation of Einstein's theory of relativity, the structure of the atom, the mysteries of quantum mechanics and cosmology. Readers will not need to search online for key terms or explanations of concepts that have been glossed over. Instead, one by one, with patience and good humor, Harris introduces each of these building blocks of our universe, taking a little time to invite readers to contemplate the momentousness of the information, as in the chapter titled nothing less than "What Is Reality?" . The watchword, here, is clarity, which Harris offers throughout, with professional illustrations and illuminating accounts of experiments and breakthroughs, offering a solid foundation for understanding and future reading Inviting and illuminating, this introduction to physics truly targets the reader who is entirely new to the subject.

Essential mathematical tools for the study of modern quantum theory.

Linear Algebra for Quantum Theory offers an excellent survey of those aspects of set theory and the theory of linear spaces and their mappings that are indispensable to the study of quantum theory. Unlike more conventional treatments, this text postpones its discussion of the binary product concept until later chapters, thus allowing many important properties of the mappings to be derived without it.

The book begins with a thorough exploration of set theory fundamentals, including mappings, cardinalities of sets, and arithmetic and theory of complex numbers. Next is an introduction to linear spaces, with coverage of linear operators, eigenvalue and the stability problem of linear operators, and matrices with special properties.

Material on binary product spaces features self-adjoint operators in a space of indefinite metric, binary product spaces with a positive definite metric, properties of the Hilbert space, and more. The final section is devoted to axioms of quantum theory formulated as trace algebra. Throughout, chapter-end problem sets help reinforce absorption of the material while letting readers test their problem-solving skills.

Ideal for advanced undergraduate and graduate students in theoretical and computational chemistry and physics, Linear Algebra for Quantum Theory provides the mathematical means necessary to access and understand the complex world of quantum theory.

The thesis gives the first experimental demonstration of a new quantum bit ("qubit") that fuses two promising physical implementations for the storage and manipulation of quantum information - the electromagnetic modes of superconducting circuits, and the spins of electrons trapped in semiconductor quantum dots - and has the potential to inherit beneficial aspects of both. This new qubit consists of the spin of an individual superconducting quasiparticle trapped in a Josephson junction made from a semiconductor nanowire. Due to spin-orbit coupling in the nanowire, the supercurrent flowing through the nanowire depends on the quasiparticle spin state. This thesis shows how to harness this spin-dependent supercurrent to achieve both spin detection and coherent spin manipulation. This thesis also represents a significant advancement to our understanding and control of Andreev levels and thus of superconductivity. Andreev levels, microscopic fermionic modes that exist in all Josephson junctions, are the microscopic origin of the famous Josephson effect, and are also the parent states of Majorana modes in the nanowire junctions investigated in this thesis. The results in this thesis are therefore crucial for the development of Majorana-based topological information processing.

"Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory". - Asher Peres Semiconductor physics is a laboratory to learn and discover the concepts of quantum mechanics and thermodynamics, condensed matter physics, and materials science, and the payoffs are almost immediate in the form of useful semiconductor devices. Debdeep Jena has had the opportunity to work on both sides of the fence - on the fundamental materials science and quantum physics of semiconductors, and in their applications in semiconductor electronic and photonic devices. In Quantum Physics of Semiconductors and Nanostructures, Jena uses this experience to make each topic as tangible and accessible as possible to students at all levels. Consider the simplest physical processes that occur in semiconductors: electron or hole transport in bands and over barriers, collision of electrons with the atoms in the crystal, or when electrons and holes annihilate each other to produce a photon. The correct explanation of these processes require a quantum mechanical treatment. Any shortcuts lead to misconceptions that can take years to dispel, and sometimes become roadblocks towards a deeper understanding and appreciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quantum mechanics, statistical physics and thermodynamics, materials science, and electromagnetism. Rarely would a student have all this background when (s)he takes a course of this nature in most universities. Jena's work fills in these gaps and gives students the background and deeper understanding of the quantum physics of semiconductors and nanostructures.

Since the beginning of the twentieth century, many experimental and theoretical works have been devoted to collisions between highly charged ions and atomic and molecular targets. It was realized that quantum mechanics is the only way, a priori, to describe such atomic phenomena. However, since quantum mechanics is very difficult to apply for collision systems with more than two particles, classical methods were very soon introduced and applied to simple collision systems and, subsequently, to more complicated systems. The results obtained by such classical methods were found to be surprisingly good, and classical mechanics is now well established, despite its approximations, as a replacement for or competition with quantum mechanics in many cases. In this book, the author will focus on the development of classical methods for describing collisional and post-collisional processes. The results will be compared with those found using quantum mechanical models, in order to demonstrate the ability of the classical approach to obtain many features and details of collision systems.

This introductory text is written for graduate students in physics taking a year-long course in quantum mechanics in which the third quarter is devoted to relativistic wave equations and field theory. Difficult concepts are introduced gradually, and the theory is applied to physically interesting problems.