The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.

Quantum-state estimation is an important field in quantum information theory that deals with the characterization of states of affairs for quantum sources. This book begins with background formalism in estimation theory to establish the necessary prerequisites. This basic understanding allows us to explore popular likelihood- and entropy-related estimation schemes that are suitable for an introductory survey on the subject. Discussions on practical aspects of quantum-state estimation ensue, with emphasis on the evaluation of tomographic performances for estimation schemes, experimental realizations of quantum measurements and detection of single-mode multi-photon sources. Finally, the concepts of phase-space distribution functions, which compatibly describe these multi-photon sources, are introduced to bridge the gap between discrete and continuous quantum degrees of freedom.This book is intended to serve as an instructive and self-contained medium for advanced undergraduate and postgraduate students to grasp the basics of quantum-state estimation. Any reader with a solid foundation in quantum mechanics, linear algebra and calculus would be able to follow the book comfortably.

The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues.Characteristically, Feynman took an untraditional non-geometric approach to gravitation and general relativity based on the underlying quantum aspects of gravity. Hence, these lectures contain a unique pedagogical account of the development of Einstein's general theory of relativity as the inevitable result of the demand for a self-consistent theory of a massless spin-2 field (the graviton) coupled to the energy-momentum tensor of matter. This approach also demonstrates the intimate and fundamental connection between gauge invariance and the principle of equivalence.

This first of a kind textbook provides computational tools in Fortran 90 that are fundamental to quantum information, quantum computing, linear algebra and one dimensional spin half condensed matter systems. Over 160 subroutines are included, and the numerical recipes are aided by detailed flowcharts. Suitable for beginner and advanced readers alike, students and researchers will find this textbook to be a helpful guide and a compendium. Key Features: Includes 160 subroutines all of which can be used either as a standalone program or integrated with any other main program without any issues. Every parameter in the input, output and execution has been provided while keeping both beginner and advanced users in mind. The output of every program is explained thoroughly with detailed examples. A detailed dependency chart is provided for every recipe.

This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990-2014.The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity - Is a Graviton Detectable? Various possible graviton-detectors are examined.This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

Providing a pedagogical introduction to the rapidly developing field of AdS/CFT correspondence, this is one of the first texts to provide an accessible introduction to all the necessary concepts needed to engage with the methods, tools and applications of AdS/CFT. Without assuming anything beyond an introductory course in quantum field theory, it begins by guiding the reader through the basic concepts of field theory and gauge theory, general relativity, supersymmetry, supergravity, string theory and conformal field theory, before moving on to give a clear and rigorous account of AdS/CFT correspondence. The final section discusses the more specialised applications, including QCD, quark-gluon plasma and condensed matter. This book is self-contained and learner-focused, featuring numerous exercises and examples. It is essential reading for both students and researchers across the fields of particle, nuclear and condensed matter physics.

The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.

In the last several decades, the quantum Hall effect has provided a remarkable platform for manipulating one-dimensional electronic modes and investigating fundamental physical phenomena. However, certain limitations make it difficult for various kinds of interesting modes structures to be formed using this platform. One example is the so called helical mode structure, in which two one-dimensional, counter propagating modes have opposite spins and thus spin and momentum are locked. Such helical modes have lately attracted significant interest, since, when coupled to a conventional superconductor, they are expected to manifest topological superconductivity and host Majorana zero modes. Even more interesting are fractional helical modes, which open the way for realizing generalized parafermionic zero modes. Possessing non-abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here we present a new platform for manipulating integer and fractional quantum Hall edge modes, which allows the formation of robust one-dimensional helical as well as fractional helical modes. The platform is based on a carefully designed double-quantum-well structure in a GaAs based system hosting two electronic sub-bands in the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed and their spin protection is verified. Beyond the formation of helical modes, the new platform can serve as a rich playground for new research. Some new possibilities include the artificial induction of compounded fractional edge modes and the construction of new edge mode-based interferometers.

In the past four decades, there has been growing interest in the exciting new topic of physics in low dimensions. Thousands of original ideas have been proposed in the literature, and some are confirmed experimentally, along with several Nobel prizes which have been awarded in this field. While there are several books available, almost all are technical and accessible only to expert researchers. This book provides an accessible introduction to the field, with less emphasis on technical details. Whilst this book does not provide a traditional history of nano-science, instead it uses simple explanations and case studies as vehicles to explain key discoveries and the importance of them, enabling readers without a background in the area to gain an understanding of some aspects of nanoscale physics. It will be of interest to researchers working in condensed matter physics, in addition to engineers and advanced students in those disciplines. It also remains accessible to 'physics enthusiasts' from other academic disciplines, as technical details are contained within boxes and footnotes which can be skipped for a general reading of the book. Features: - Provides an accessible introduction to a technical subject - Contains exciting developments from the cutting-edge science being conducted in the area - Authored by a recognised expert in the field

The core content of even the most intricate intellectual edifices is often a simple fact or idea. So is it with quantum mechanics; the entire mathematical fabric of the formal description of quantum mechanics stems essentially from the fact that quantum probabilities interfere (i.e., from the superposition principle). This book is dedicated to substantiating this claim. In the process, the book tries to demonstrate how the factual content of quantum mechanics can be transcribed in the formal language of vector spaces and linear transformations by disentangling the empirical content from the usual formal description. More importantly, it tries to bring out what this transcription achieves. The book uses a pedagogic strategy which reverse engineers the postulates of quantum mechanics to device a schematic outline of the empirical content of quantum mechanics from which the postulates are then reconstructed step by step. This strategy is adopted to avoid the disconcerting details of actual experiments (however simplified) to spare the beginner of issues that lurk in the fragile foundations of the subject. In the Copenhagen interpretation of quantum mechanics, the key idea is measurement. But "measurement" carries an entirely different meaning from the connotation that the term carries elsewhere in physics. This book strives to underline this as strongly as possible. The book is intended as an undergraduate text for a first course in quantum mechanics. Since the book is self contained, it may also be used by enthusiastic outsiders interested to get a glimpse of the core content of the subject. Features: Demonstrates why linear algebra is the appropriate mathematical language for quantum mechanics. Uses a reconstructive approach to motivate the postulates of quantum mechanics. Builds the vocabulary of quantum mechanics by showing how the entire body of its conceptual ingredients can be constructed from the single notion of quantum measurement.

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit."

This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990-2014.The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity - Is a Graviton Detectable? Various possible graviton-detectors are examined.This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

This book is a collection of lecture notes and contributions in "Summer School on Diversities in Quantum Computation/Information" held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.

This book covers a range of new research on computational quantum chemistry, along with a special section devoted to exotic carbon allotropes and spiro quantum theory. The section on spiro quantum theory covers the technical presentation of the ideas surrounding the emergence of a synthetic, analytical, and theoretical spiro quantum chemistry edifice, as well as a chemical topology scheme that successfully describes molecules and patterns, including the hydrocarbons and allotropes of carbon. The second part of the book covers a range of new research on computational quantum chemistry.

Over the course of the past two to three decades, new tools of presentation and mathematical treatment have emerged and the subject matter of quantum mechanics has gone through significant changes. A Textbook on Modern Quantum Mechanics presents the selected elementary, intermediate, and advance topics with rejuvenated approach to the subject matter. Newly merged topics from contemporary physics and chemistry are included in the text as well as solved examples. The book covers: (i) fundamental discoveries that are the foundation of modern quantum mechanics; (ii) solution of Schroedinger's wave equation for 1D problems and their importance; (iii) matrix and vector formulation of quantum mechanics; (iv) transformations, symmetries, and conservation laws; (v) angular and spin momenta; (vi) solution of Schroedinger equation for central potentials; (vii) time-independent perturbation theory, variational method and WKB approximation; (viii) quantum theory of scattering; (xi) many-particle systems and their quantum mechanical treatments; (x) time-dependent perturbations and the interaction of fields with matter; (xi) relativistic quantum mechanics; and (xii) quantization of fields and the second quantization. Key Features: It provides everything a student needs to know for succeeding at all levels of the undergraduate and graduate studies. It covers most of the topics that are taught under (a) elementary, (b) intermediate, and (c) advance courses of quantum mechanics at universities and colleges. It has detailed and elegant mathematical treatment with contemporary style of interpretation and presentation in simple English. Solved examples and unsolved exercises that are part of each chapter to consolidate the readers' understanding of fundamental concepts. The subject matter of the book is well tested on the students taught by the author over a period of 30 years. This is a valuable textbook for students pursuing Bachelor of Science, Master of Science, and Doctor of Philosophy (PhD) degrees in the subjects of Physics, Chemistry, and materials science in India, South Asian countries, the United States, and Europe.

Quantum-state estimation is an important field in quantum information theory that deals with the characterization of states of affairs for quantum sources. This book begins with background formalism in estimation theory to establish the necessary prerequisites. This basic understanding allows us to explore popular likelihood- and entropy-related estimation schemes that are suitable for an introductory survey on the subject. Discussions on practical aspects of quantum-state estimation ensue, with emphasis on the evaluation of tomographic performances for estimation schemes, experimental realizations of quantum measurements and detection of single-mode multi-photon sources. Finally, the concepts of phase-space distribution functions, which compatibly describe these multi-photon sources, are introduced to bridge the gap between discrete and continuous quantum degrees of freedom.This book is intended to serve as an instructive and self-contained medium for advanced undergraduate and postgraduate students to grasp the basics of quantum-state estimation. Any reader with a solid foundation in quantum mechanics, linear algebra and calculus would be able to follow the book comfortably.

The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.

Quantum Theory: Density, Condensation, and Bonding presents in a unitary manner the main actual theories of matter, mainly the density function theory (DFT) for fermions, the Bose-Einstein condensation (BEC) for bosons, and chemical bonding as a special realization of the first two so-called mixed fermionic-bosonic states. The book covers the modern and ultimately developed quantum theories involving the key concepts of density, condensation, and bonding. The book compiles, for the first time, the density functional theory with Bose-Einstein condensation and chemical bonding theories in a fresh and novel perspective. The book introduces modern theories of matter structure and explains the nature of chemical bonds under the consecrated and ultimate quantum paradigms of molecular structure. The book is divided into three parts, one for each level of studies: Part I: Primer Density Functional Theory is suitable for undergraduate introductory courses in physics, chemistry, and the natural sciences. Part II: Primer Density Functional Bose-Einstein Condensation Theory would be suitable for graduate- or master-level courses in physics or natural sciences. Part III: Modern Quantum Theories of Chemical Bonding is written for the post-graduate, master or doctorate courses on quantum structure of molecules in chemistry or natural sciences. Thus, this book is organized as a succession of three linked courses, from undergraduate, to graduate, to postgraduate levels in modern quantum theories of many-body systems. It covers three main concepts: density, condensation, and bonding and contains the most celebrated and challenging theories of matter. The book provides a fresh perspective on the quantum theory of structure of physico-chemical systems and will show students at all levels and researchers the way for future elaboration and discoveries toward the unification of the physical and chemical concepts of matter.

This is the solution manual for Riazuddin's and Fayyazuddin's Quantum Mechanics (2nd edition). The questions in the original book were selected with a view to illustrate the physical concepts and use of mathematical techniques which show their universality in tackling various problems of different physical origins. This solution manual contains the text and complete solution of every problem in the original book. This book will be a useful reference for students looking to master the concepts introduced in Quantum Mechanics (2nd edition).

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He then goes on to apply the renormalization group to selected problems, with emphasis on the underlying physics and the basic assumptions involved.

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.

The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface.The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.