It is now generally accepted that quantum mechanics occupies a central place in microscopic physical theory. The importance of this discipline shows up in the research journals, and also in the graduate physics curriculum. Not only is quantum mechanics a required subject, both for experimental and theoretical students; it appears as well to be influencing the way in which classical physics is taught. Presentations of classical mechanics that slight the traditional problems of planetary motion, unsymmetrical tops and dissipative systems in favor of collision theory and Poisson brackets are becoming more and more prevalent. With the much younger subject of classical electrodynamics, the analogous tendency is less marked, although here again emphasis is being placed on those examples that bring the student closest to the formalism of quantum electrodynamics. Such trends are of course proper and reasonable, especially so long as no important classical ideas are omitted from consideration. Indeed, the study of acoustics, hydrodynamics, and elasticity probably benefits from an early introduction of field concepts.
It is now generally accepted that quantum mechanics occupies a central place in microscopic physical theory. The importance of this discipline shows up in the research journals, and also in the graduate physics curriculum. Not only is quantum mechanics a required subject, both for experimental and theoretical students; it appears as well to be influencing the way in which classical physics is taught. Presentations of classical mechanics that slight the traditional problems of planetary motion, unsymmetrical tops and dissipative systems in favor of collision theory and Poisson brackets are becoming more and more prevalent. With the much younger subject of classical electrodynamics, the analogous tendency is less marked, although here again emphasis is being placed on those examples that bring the student closest to the formalism of quantum electrodynamics. Such trends are of course proper and reasonable, especially so long as no important classical ideas are omitted from consideration. Indeed, the study of acoustics, hydrodynamics, and elasticity probably benefits from an early introduction of field concepts.
Quantum mechanics to a large extent is a subject which conceptually is abstract and very mathematical in nature. Despite its abstract formalism it has proved to be a storehouse of ideas of enormous practical value. These radically new ideas, boldly proposed and strikingly uncommon, have helped to unlock deep secrets of the world, especially at the microscopic level where the breakdown of classical physics becomes rather apparent. There flows indeed from this subject a vast stream of concrete, everyday life applications. The phenomenon of transistors, television, semiconductors, computers, lasers, to name a few, instruments of unde-bated importance for communication, education, energy requirements, medicine, etc.—all involve quantum mechanical effects. The work of P. Lenard and especially of A. Einstein on the photoelectric effect, for example, helped toward the development of television. Our world has been positively changed by the fruits of this elegant subject and its forward thinking founders.
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
Since its emergence in the early twentieth century, quantum theory has become the fundamental physical paradigm, and is essential to our understanding of the world. Providing a deeper understanding of the microscopic world through quantum theory, this supplementary text reviews a wider range of topics than conventional textbooks. Emphasis is given to modern entanglement, quantum teleportation, and Bose-Einstein condensation. Macroscopic quantum effects of practical relevance, for example superconductivity and the quantum Hall effect, are also described. Looking to the future, the author discusses the exciting prospects for quantum computing. Physical, rather than formal, explanations are given, and mathematical formalism is kept to a minimum so readers can understand the concepts more easily. Theoretical discussions are combined with a description of the corresponding experimental results. This book is ideal for undergraduate and graduate students in quantum theory and quantum optics.
Students and instructors alike will find this organized and detailed approach to quantum mechanics ideal for a two-semester graduate course on the subject. This textbook covers, step-by-step, important topics in quantum mechanics, from traditional subjects like bound states, perturbation theory and scattering, to more current topics such as coherent states, quantum Hall effect, spontaneous symmetry breaking, superconductivity, and basic quantum electrodynamics with radiative corrections. The large number of diverse topics are covered in concise, highly focused chapters, and are explained in simple but mathematically rigorous ways. Derivations of results and formulae are carried out from beginning to end, without leaving students to complete them. With over 200 exercises to aid understanding of the subject, this textbook provides a thorough grounding for students planning to enter research in physics. Several exercises are solved in the text, and password-protected solutions for remaining exercises are available to instructors at www.cambridge.org/9780521877602.
Abstract It can easily be argued that a fully mature and complete knowledge of quantum mechanics should include historical, axiomatic, formal mathematical, and even philosophical background to the subject. However, for a student approaching quantum theory for the first time in a serious way, it can be the case that an approach utilizing his or her existing knowledge of, and intuition for, classical physics (including mechanics, wave physics, and electricity and magnetism) as well as emphasizing connections to experimental results can be the most pro- ductive. That, at least, is the point of view adopted in this text and can be illustrated by a focus on the following general topics: