This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schroedinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.

The first version of quantum theory, developed in the mid 1920's, is what is called nonrelativistic quantum theory; it is based on a form of relativity which, in a previous volume, was called Newton relativity. But quickly after this first development, it was realized that, in order to account for high energy phenomena such as particle creation, it was necessary to develop a quantum theory based on Einstein relativity. This in turn led to the development of relativistic quantum field theory, which is an intrinsically many-body theory. But this is not the only possibility for a relativistic quantum theory. In this book we take the point of view of a particle theory, based on the irreducible representations of the Poincare group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; we develop what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A central issue in any relativistic quantum theory is how to introduce interactions without spoiling relativistic invariance. We show that interactions can be incorporated in a mass operator, in such a way that relativistic invariance is maintained. Surprisingly for a relativistic theory, such a construction allows for instantaneous interactions; in addition, dynamical particle exchange and particle production can be included in a multichannel formulation of the mass operator. For systems of more than two particles, however, straightforward application of such a construction leads to the undesirable property that clusters of widely separated particles continue to interact with one another, even if the interactions between the individual particles are of short range. A significant part of this volume deals with the solution of this problem. Since relativistic quantum mechanics is not as well-known as relativistic quantum field theory, a chapter is devoted to applications of point form quantum mechanics to nuclear physics; in particular we show how constituent quark models can be used to derive electromagnetic and other properties of hadrons.

Somewhere near the heart of existence, shimmers the ethereal beauty of the mystery of Time. Though seemingly familiar to us all, time harbours secrets that penetrate the very deepest levels of reality, and though we feel certain in our conviction that we're swept forth upon the crest of its never-ending flow, with Einstein's discovery of relativity came what is perhaps the most stunning realisation in the entire history of scientific thought - the wondrously breathtaking revelation that in reality, there's actually no such thing as the passage of time... How can this extraordinary truth be reconciled with the reality we so surely suppose to experience? What does it mean for the very human concerns of life and death, free will, identity, and self? What should it mean for our philosophy? And how should it inform our world view? The search for answers leads through the fantastical realm of quantum physics, and the strange parallel worlds it describes, as we discover that the answers which such questions provoke, are perhaps even more profound than the questions themselves. Buried deep within the riddle of time, lies the staggering beauty of the world. As we peel back the layers to try and sneak a glimpse into eternity, we find a light shining not only upon the nature of reality, but on the nature of ourselves...

By incorporating extensive student input and innovative teaching methodologies, this book aims to make the process of learning quantum field theory easier, and thus more rapid, profound, and efficient, for both students and instructors. Comprehensive explanations are favored over conciseness, every step in derivations is included, and 'big picture' overviews are provided throughout.
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The book focuses on the canonical quantization approach, but also provides an introductory chapter on path integrals. It covers fundamental principles of quantum field theory, then develops quantum electrodynamics in depth. The second edition incorporates suggestions from readers to make certain sections even clearer and easier to understand.
See the first few chapters at www.quantumfieldtheory.info.

"Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems "is intended for scientists and graduate students interested in the foundations of quantum mechanics and applied scientists interested in accurate atomic and molecular models. This is a reference to those working in the new field of relativistic optics, in topics related to relativistic interactions between very intense laser beams and particles, and is based on 30 years of research. The novelty of this work consists of accurate connections between the properties of quantum equations and corresponding classical equations used to calculate the energetic values and the symmetry properties of atomic, molecular and electrodynamical systems, as well as offering applications using methods for calculating the symmetry properties and the energetic values of systems and the calculation of properties of high harmonics in interactions between very intense electromagnetic fields and electrons.
Features detailed explanations of the theories of atomic and molecular systems, as well as wave properties of stationary atomic and molecular systemsProvides periodic solutions of classical equations, semi-classical methods, and theories of systems composed of very intense electromagnetic fields and particles Offers models and methods based on 30 years of research

Our understanding of subatomic particles developed over many years, although a clear picture of the different particles, their interactions and their inter-relationships only emerged in the latter part of the twentieth century. The first ""subatomic particles"" to be investigated were those which exhibit readily observable macroscopic behavior, specifically these are the photon, which we observe as light and the electron, which is manifested as electricity. The true nature of these particles, however, only became clear within the last century or so. The development of the Standard Model provided clarification of the way in which various particles, specifically the hadrons, relate to one another and the way in which their properties are determined by their structure. The final piece, perhaps, of the final model, that is the means by which some particles acquire mass, has just recently been clarified with the observation of the Higgs boson. Since the 1970s it has been known that the measured solar neutrino flux was inconsistent with the flux predicted by solar models. The existence of neutrinos with mass would allow for neutrino flavor oscillations and would provide an explanation for this discrepancy. Only in the past few years, has there been clear experimental evidence that neutrinos have mass. The description of particle structure on the basis of the Standard Model, along with recent discoveries concerning neutrino properties, provides us with a comprehensive picture of the properties of subatomic particles. Part I of the present book provides an overview of the Standard Model of particle physics including an overview of the discovery and properties of the Higgs boson. Part II of the book summarizes the important investigations into the physics of neutrinos and provides an overview of the interpretation of these studies.

Randomness is an active element relevant to all scientific activities. The book explores the way in which randomness suffuses the human experience, starting with everyday chance events, followed by developments into modern probability theory, statistical mechanics, scientific data analysis, quantum mechanics, and quantum gravity. An accessible introduction to these theories is provided as a basis for going into deeper topics.Fowler unveils the influence of randomness in the two pillars of science, measurement and theory. Some emphasis is placed on the need and methods for optimal characterization of uncertainty. An example of the cost of neglecting this is the St. Petersburg Paradox, a theoretical game of chance with an infinite expected payoff value. The role of randomness in quantum mechanics reveals another particularly interesting finding: that in order for the physical universe to function as it does and permit conscious beings within it to enjoy sanity, irreducible randomness is necessary at the quantum level.The book employs a certain level of mathematics to describe physical reality in a more precise way that avoids the tendency of nonmathematical descriptions to be occasionally misleading. Thus, it is most readily digested by young students who have taken at least a class in introductory calculus, or professional scientists and engineers curious about the book's topics as a result of hearing about them in popular media. Readers not inclined to savor equations should be able to skip certain technical sections without losing the general flow of ideas. Still, it is hoped that even readers who usually avoid equations will give those within these pages a chance, as they may be surprised at how potentially foreboding concepts fall into line when one makes a legitimate attempt to follow a succession of mathematical implications.

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 detail the mathematical methods needed to do working applications in molecular quantum mechanics, as a preliminary step before using commercial programmes doing quantum chemistry calculations. This book aims to bridge the gap between the classic Coulson s Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny s Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter.
* Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics
* Simplifies all mathematical formulae for the reader
* Provides educational training in basic methodology"

This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text, aimed at graduate level physics students with a working knowledge of quantum mechanics and statistical physics, provides a brief overview of the development of classical thermodynamics and its quantum formulation in Chapter 1. Chapter 2 then explores typical thermodynamic settings, such as cycles and work extraction protocols, when the working material is genuinely quantum. Finally, Chapter 3 explores the thermodynamics of quantum information processing and introduces the reader to some more state of-the-art topics in this exciting and rapidly developing research field.

This textbook is a unique and ambitious primer of nuclear physics, which introduces recent theoretical and experimental progresses starting from basics in fundamental quantum mechanics. The highlight is to offer an overview of nuclear structure phenomena relevant to recent key findings such as unstable halo nuclei, superheavy elements, neutron stars, nucleosynthesis, the standard model, lattice quantum chromodynamics (LQCD), and chiral effective theory. An additional attraction is that general properties of nuclei are comprehensively explained from both the theoretical and experimental viewpoints. The book begins with the conceptual and mathematical basics of quantum mechanics, and goes into the main point of nuclear physics - nuclear structure, radioactive ion beam physics, and nuclear reactions. The last chapters devote interdisciplinary topics in association with astrophysics and particle physics. A number of illustrations and exercises with complete solutions are given. Each chapter is comprehensively written starting from fundamentals to gradually reach modern aspects of nuclear physics with the objective to provide an effective description of the cutting edge in the field.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang-Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg-Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the -deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

2013 Winner (Gold Medal), Classical Studies/Philosophy, Independent Publisher Book Awards -- 2013 Winner, Spirituality: General, International Book Awards -- 2013 Winner, Science, National Indie Excellence Awards -- 2013 Finalist, Science: General, International Book Awards -- 2013 Finalist, Best New Non-Fiction, International Book Awards -- 2013 Finalist, Best Cover Design: Non-Fiction, International Book Awards -- 2013 Finalist, Philosophy, National Indie Excellence Awards -- The Eternal Law takes the reader on a fascinating journey through some of the most profound questions related to our understanding of modern science. What does it mean to say that there is an eternal mathematical law underpinning all of physical reality? How must we expand our narrow conception of science to include not only logic but also intuition, consciousness, and the pursuit of beauty, symmetry, simplicity, and unity? Is truth objective, or is it nothing more than a whimsical projection of opinions? Why were many of the key founders of modern science inevitably drawn to ancient Greek philosophy? Spencer's extraordinary clarity helps to restore a sane vision of reality, while deepening our appreciation of what Einstein called 'the mysterious'.

This book is the first comprehensive book about reservoir computing (RC). RC is a powerful and broadly applicable computational framework based on recurrent neural networks. Its advantages lie in small training data set requirements, fast training, inherent memory and high flexibility for various hardware implementations. It originated from computational neuroscience and machine learning but has, in recent years, spread dramatically, and has been introduced into a wide variety of fields, including complex systems science, physics, material science, biological science, quantum machine learning, optical communication systems, and robotics. Reviewing the current state of the art and providing a concise guide to the field, this book introduces readers to its basic concepts, theory, techniques, physical implementations and applications. The book is sub-structured into two major parts: theory and physical implementations. Both parts consist of a compilation of chapters, authored by leading experts in their respective fields. The first part is devoted to theoretical developments of RC, extending the framework from the conventional recurrent neural network context to a more general dynamical systems context. With this broadened perspective, RC is not restricted to the area of machine learning but is being connected to a much wider class of systems. The second part of the book focuses on the utilization of physical dynamical systems as reservoirs, a framework referred to as physical reservoir computing. A variety of physical systems and substrates have already been suggested and used for the implementation of reservoir computing. Among these physical systems which cover a wide range of spatial and temporal scales, are mechanical and optical systems, nanomaterials, spintronics, and quantum many body systems. This book offers a valuable resource for researchers (Ph.D. students and experts alike) and practitioners working in the field of machine learning, artificial intelligence, robotics, neuromorphic computing, complex systems, and physics.

In this thesis, the first measurement of the running of the top quark mass is presented. This is a fundamental quantum effect that had never been studied before. Any deviation from the expected behaviour can be interpreted as a hint of the presence of physics beyond the Standard Model. All relevant aspects of the analysis are extensively described and documented. This thesis also describes a simultaneous measurement of the inclusive top quark-antiquark production cross section and the top quark mass in the simulation. The measured cross section is also used to precisely determine the values of the top quark mass and the strong coupling constant by comparing to state-of-the-art theoretical predictions. All the theoretical and experimental aspects relevant to the results presented in this thesis are discussed in the initial chapters in a concise but complete way, which makes the material accessible to a wider audience.

This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schroedinger equation is a complex-valued evolution equation and the Schroedinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.

This book presents quantum theory as a theory based on new relationships among matter, thought, and experimental technology, as against those previously found in physics, relationships that also redefine those between mathematics and physics in quantum theory. The argument of the book is based on its title concept, reality without realism (RWR), and in the corresponding view, the RWR view, of quantum theory. The book considers, from this perspective, the thinking of Bohr, Heisenberg, Schroedinger, and Dirac, with the aim of bringing together the philosophy and history of quantum theory. With quantum theory, the book argues, the architecture of thought in theoretical physics was radically changed by the irreducible role of experimental technology in the constitution of physical phenomena, accordingly, no longer defined independently by matter alone, as they were in classical physics or relativity. Or so it appeared. For, quantum theory, the book further argues, made us realize that experimental technology, beginning with that of our bodies, irreducibly shapes all physical phenomena, and thus makes us rethink the relationships among matter, thought, and technology in all of physics.

An understanding of the effects of electronic correlations in quantum systems is one of the most challenging problems in physics, partly due to the relevance in modern high technology. Yet there exist hardly any books on the subject which try to give a comprehensive overview on the field covering insulators, semiconductors, as well as metals. The present book tries to fill that gap.It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics. The reader will have a better understanding of the great progress which has been made in the field over the past few decades.

Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice.

This book is ideal for the electronics, photonics and computer engineer who requires an easy- to-understand foundation on the principles of quantum information processing and quantum error correction, together with insight into how to develop quantum electronic and photonic circuits.

Readers of this book will be ready for further study in this area, and will be prepared to perform independent research. The reader completed the book will be able design the information processing circuits, stabilizer codes, Calderbank-Shor-Steane (CSS) codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The reader completed the book will be proficient in quantum fault-tolerant design as well.

Unique Features

Unique in covering both quantum information processing and quantum error correction - everything in one book that an engineer needs to understand and implement quantum-level circuits.

Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics.

In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits.

Provides the right balance among the quantum mechanics, quantum error correction, quantum computing and quantum communication.

Dr. Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering of College of Engineering, University of Arizona, with a joint appointment in the College of Optical Sciences. Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol, Bristol, UK; Tyco Telecommunications, Eatontown, USA; and National Technical University of Athens, Athens, Greece. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction. He presently directs the Optical Communications Systems Laboratory (OCSL) within the ECE Department at the University of Arizona.
Provides everything an engineer needs in one tutorial-based introduction to understand and implement quantum-level circuitsAvoids the heavy use of mathematics by not assuming the previous knowledge of quantum mechanicsProvides in-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits

This book is a thoroughly modern and highly pedagogical graduate-level introduction to quantum optics, a subject which has witnessed stunning developments in recent years and has come to occupy a central role in the 'second quantum revolution'. The reader is invited to explore the fundamental role that quantum optics plays in the control and manipulation of quantum systems, leading to ultracold atoms, circuit QED, quantum information science, quantum optomechanics, and quantum metrology. The building blocks of the subject are presented in a sequential fashion, starting from the simplest physical situations before moving to increasingly complicated ones. This pedagogically appealing approach leads to quantum entanglement and measurement theory being introduced early on and before more specialized topics such as cavity QED or laser cooling. The final chapter illustrates the power of scientific cross-fertilization by surveying cutting-edge applications of quantum optics and optomechanics in gravitational wave detection, tests of fundamental physics, searches for dark matter, geophysical monitoring, and ultraprecise clocks. Complete with worked examples and exercises, this book provides the reader with enough background knowledge and understanding to follow the current journal literature and begin producing their own original research.

Electrostatic Accelerators have been at the forefront of modern technology since the development by Sir John Cockroft and Ernest Walton in 1932 of the first accelerator, which was the first to achieve nuclear transmutation and earned them the Nobel Prize in Physics in 1951. The applications of Cockroft and Walton's development have been far reaching, even into our kitchens where it is employed to generate the high voltage needed for the magnetron in microwave ovens. Other electrostatic accelerator related Nobel prize winning developments that have had a major socio-economic impact are; the electron microscope where the beams of electrons are produced by an electrostatic accelerator, X-rays and computer tomography (CT) scanners where the X-rays are produced using an electron accelerator and microelectronic technology where ion implantation is used to dope the semiconductor chips which form the basis of our computers, mobile phones and entertainment systems. Although the Electrostatic Accelerator field is over 90 years old, and only a handful of accelerators are used for their original purpose in nuclear physics, the field and the number of accelerators is growing more rapidly than ever. The objective of this book is to collect together the basic science and technology that underlies the Electrostatic Accelerator field so it can serve as a handbook, reference guide and textbook for accelerator engineers as well as students and researchers who work with Electrostatic Accelerators.