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Featuring new coverage of quantum engineering and quantum information processing, the third edition of this bestselling textbook continues to provide a uniquely practical introduction to the fundamentals of quantum mechanics. It features straightforward explanations of quantum effects, suitable for readers from all backgrounds; real-world engineering problems showcasing the practical application of theory to practice, providing a relevant and accessible introduction to cutting-edge quantum applications; over 60 accessible worked examples using MATLAB (as well as open-source Python), allowing deepened understanding through computational exploration and visualization; and a new chapter on quantum engineering, introducing state-of-the-art concepts in quantum information processing and quantum device design. Updated throughout and supported online by downloadable MATLAB code, exam questions, and solutions to over 150 homework problems for instructors, this is the ideal textbook for senior undergraduate and graduate students in applied science, applied physics, engineering, and materials science studying a first course in quantum mechanics.
This book offers an accessible and engaging introduction to quantum cryptography, assuming no prior knowledge in quantum computing. Essential background theory and mathematical techniques are introduced and applied in the analysis and design of quantum cryptographic protocols. The title explores several important applications such as quantum key distribution, quantum money, and delegated quantum computation, while also serving as a self-contained introduction to the field of quantum computing. With frequent illustrations and simple examples relevant to quantum cryptography, this title focuses on building intuition and challenges readers to understand the basis of cryptographic security. Frequent worked examples and mid-chapter exercises allow readers to extend their understanding, and in-text quizzes, end-of-chapter homework problems, and recommended further reading reinforce and broaden understanding. Online resources available to instructors include interactive computational problems in Julia, videos, lecture slides, and a fully worked solutions manual.
The ideal text for a two-semester graduate course on quantum mechanics. Fresh, comprehensive, and clear, it strikes the optimal balance between covering traditional material and exploring contemporary topics. Focusing on the probabilistic structure of quantum mechanics and the central role of symmetries to unify principles, this textbook guides readers through the logical development of the theory. Students will also learn about the more exciting and controversial aspects of quantum theory, with discussions on past interpretations and the current debates on cutting-edge concepts such as quantum information and entanglement, open quantum systems, and quantum measurement theory. The book has two types of content: Type A material is more elementary and is fully self-contained, functioning like a separate book within the book, while Type B content is at the level of a graduate course. Requiring minimal physics background, this textbook is appropriate for mathematics and engineering students, in addition to physicists. Introducing cutting-edge topics in the field, the book features about 150 concept-checking questions, 300 homework problems and a solutions manual.
We assume that the electron carries quantised angular momentum as it moves around the positively charged proton in the hydrogen atom. This leads to a quantisation of the total energy of the electron. The Bohr model is a semiclassical model, combining classical orbits with the idea of quantising a physical quantity. This model explains some of the features of the real hydrogen atom (e.g. energy quantisation), but fails to explain other properties, such as the shape and the related binding properties.
The state of a quantum-mechanical system can be described by a wave function or a state ket. Each wave function is defined in a specific space (e.g. in the position or momentum space). Conversely, the state kets do not require a specific space. The terms ‘bra’ and ‘ket’ are derived from the word ‘bracket’.
In classical physics, a distinction is made between two different concepts: waves and particles. However, various experiments have shown that this strict distinction must be replaced by a new concept.
In mathematical terms, an operator transforms a given function into a new function. To better understand operators, we summarise the analogies with matrices below.
An approximate solution can be derived from the Schrödinger equation, if the amplitude of the wave function changes only slowly relative to the phase. This procedure is called the Wentzel–Kramers–Brillouin approximation.
Quantum Mechanics will enthuse graduate students and researchers and equip them with effective methodologies for challenging applications in atomic, molecular, and optical sciences and in condensed matter and nuclear physics also. This book attempts to make fundamental principles intuitively appealing. It will assist readers in learning difficult methods. Exposition of fundamental principles includes a discussion on position-momentum and energy-time uncertainty, angular momentum algebra, parity, bound and unbound eigenstates of an atom, approximation methods, time-reversal symmetry in collisions, and on a measurable time delay in scattering. It also provides an early introduction to Feynman path integrals and to geometric phase. A novel Lambert-W method to solve quantum mechanical problems is also introduced. It seeks to enable readers gain confidence in applying methods of non-relativistic and relativistic quantum theory rigorously to problems on atomic structure and dynamics, spectroscopy and quantum collisions, and problems on introductory quantum information processing and computing.
We introduce the task of key distribution, whose goal is to allow two mutually trusting users, Alice and Bob, to generate a random shared key that is unknown to any eavesdropper in the protocol. We start by precisely defining this task and our model for adversaries. We then show how to realize it in a simple toy scenario, which will help us demonstrate the key ideas. Finally we introduce information reconciliation, which is an important building block in the protocols that we will study in subsequent chapters.