Lectures on Quantum State Estimation (1版)

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【簡介】 This is the 7th book in the author’s ＂Lectures on ...＂ book series, and the first aimed at graduate-level readers (two additional graduate texts are in preparation). Primarily intended for physics graduate students, the book is accessible to advanced undergraduates and will appeal to students with a background in statistics and a keen interest in quantum physics. By the end of this book, readers will be well-prepared for working on research projects that require the drawing of inference from the noisy data collected in quantum experiments, as epitomized by quantum state estimation.The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators (＂best guesses＂) with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author’s courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author’s group at CQT and presents this material in textbook form for the first time.

Fluid Mechanics: Volume 4: Lectures on Theoretical Physics (1版)

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【簡介】 Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

Quantum Mechanics: Volume 3: Lectures on Theoretical Physics (1版)

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【簡介】 The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.

Electromagnetism: Volume 2: Lectures on Theoretical Physics (1版)

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【簡介】 There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like. This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.

Classical Mechanics: Volume 1: Lectures on Theoretical Physics (1版)

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【簡介】 Any education in theoretical physics begins with the laws of classical mechanics. The basics of the subject were laid down long ago by Galileo and Newton and are enshrined in the famous equation F=ma that we all learn in school. But there is much more to the subject and, in the intervening centuries, the laws of classical mechanics were reformulated to emphasis deeper concepts such as energy, symmetry, and action. This textbook describes these different approaches to classical mechanics, starting with Newton’s laws before turning to subsequent developments such as the Lagrangian and Hamiltonian approaches. The book emphasises Noether’s profound insights into symmetries and conservation laws, as well as Einstein’s vision of spacetime, encapsulated in the theory of special relativity. Classical mechanics is not the last word on theoretical physics. But it is the foundation for all that follows. The purpose of this book is to provide this foundation.