The book contains four chapters. The first one deals with elementary problems of one dimensional quantum mechanics of scalar particles, and their solution is given by much more simpler method than in standard textbooks. Attention should be paid to problems with periodic potentials. In the second chapter methods of one-dimensional quantum mechanics are applied to three-dimensional scattering problems. Here a new approach to the dynamic diffraction theory based on multiple wave scattering method is proposed. Diffraction on a crystalline plane is solved exactly, and is shown to vanish in contradiction with experimental observations. In the third chapter, all the problems of the first one are generalized to spinor particles. The most interesting questions are related to polarization of particles and rotation of polarization by means of radio-frequency fields, which create superpositions of states with different energies and speeds. The fourth chapter is devoted to fundamental questions of quantum mechanics. The theory of weak measurements is criticized. Some experiments related to wave packets and to determination of quantization axis of non polarized neutron beams are proposed.
The book contains four chapters. The first one deals with elementary problems of one dimensional quantum mechanics of scalar particles, and their solution is given by much more simpler method than in standard textbooks. Attention should be paid to problems with periodic potentials. In the second chapter methods of one-dimensional quantum mechanics are applied to three-dimensional scattering problems. Here a new approach to the dynamic diffraction theory based on multiple wave scattering method is proposed. Diffraction on a crystalline plane is solved exactly, and is shown to vanish in contradiction with experimental observations. In the third chapter, all the problems of the first one are generalized to spinor particles. The most interesting questions are related to polarization of particles and rotation of polarization by means of radio-frequency fields, which create superpositions of states with different energies and speeds. The fourth chapter is devoted to fundamental questions of quantum mechanics. The theory of weak measurements is criticized. Some experiments related to wave packets and to determination of quantization axis of non polarized neutron beams are proposed.
After a short review of some essential concepts of classical physics (with a discussion of the so-called `scientific method', which is rarely found in textbooks of this kind), including the classical description of particles and waves, together with a sketch of statistical thermodynamics, the basics of quantum mechanics are introduced. The third chapter then treats systems of identical particles and their statistics, as well as the statistics of discrete energy levels. This is followed by an extensive presentation of the behaviour of quantum particles in periodic potentials with obvious applications to crystalline materials, including metals, insulators, semiconductors and superconductors. The band structure of some special materials, intrinsic carrier concentrations and electrons in metals are further topics of this main chapter. In most quantum mechanics textbooks the subjects of the fifth chapter, quantum wells, harmonic oscillators and the hydrogen atom, are usually introduced before a discussion of periodic potentials, but the author's exposition makes it quite plausible to place them afterwards. The concept of tunnelling through potential barriers and important application examples, ranging from ohmic contacts to scanning tunnelling microscopy and even radioactivity, make up the next chapter. Some approximation methods, i.e. stationary perturbation theory with applications to coupled wells, and the variational method, are treated in the next chapter. The final chapter dealing with quantum mechanics then is concerned with scattering and collision problems, again, of course, with examples from solid state physics. This last chapter, however, looks somehow merely added on, since it introduces only quite briefly the theory of special relativity -almost certainly in order not to leave out this important revolution of modern physics. Three appendices, on Fermi's Golden Rule, Boltzmann's transport theory and quantum interference devices, round off the contents. The book abounds with links to modern technologies that have evolved out of quantum mechanics (with, of course, the exception of the last chapter on special relativity). To the reviewer this constitutes its outstanding value as a textbook on quantum mechanics for engineering students. In addition, about 100 solved numerical examples in the text illustrate very lucidly some of the more abstract concepts, and at the end of the chapters altogether 200 further problems are posed. Although some of the concepts and results of quantum mechanics are introduced in a seemingly ad hoc manner, nevertheless the book as a whole certainly represents a valuable teaching tool at engineering schools; even physics majors may profit from the wealth of technical applications not usually found in their textbooks on quantum mechanics.
This book and the accompanying software (PC Diskette) is a toolbox for performing a set of numerical simulations on simple quantum mechanical problems. It is one in a series of similar books (CUPS) covering different fields in physics from classical mechanics to nuclear and particle physics. Each chapter of the book is written by a different author and deals with a different physical problem. The choice of problems is standard, e.g. bound state and scattering problems in one and three dimensions, quantum mechanical time development; the exceptions are, a study of identical particles and electron states in a one dimensional lattice, an example from solid state physics. Although the chapters are self-contained and can be studied independently (at the expense of some minor duplication of material), care was taken with a uniform style of presentation and similar format in numerical simulations. As a result, it is easy to proceed in the study of the different problems having understood the technical possibilities of one simulation. Each chapter starts with a section presenting the basic theoretical concepts to be studied using the numerical simulation. It is followed by a section with a short description of the numerical technique used and an extensive series of suggestions for problems and quantities to experiment with, using the computer codes provided. A final section describes in detail how to run the computer programs. This book is not, and is not intended to be, a textbook for learning quantum mechanics nor a textbook of numerical analysis. Nevertheless, I find the theoretical presentation clear and straightforward enough for its purpose. The extensive and up to date list of references to books and research articles at the end of each chapter is also very helpful. Technically, I found the software easy to install and, after some initial testing, easy to run. The produced plots are clear and the use of units of atomic dimension gives a touch of reality to the simulations. In contrast to other similar books, this is not a `picture' book of quantum mechanics where results of numerical simulations are illustrated; here the reader is given the necessary means to play and discover for himself the properties of quantum mechanical systems. I believe that this book, used by teachers for demonstrations and students for independent study, provides a versatile tool for numerical experimentation in quantum mechanics.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
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
The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivations and explanations. The basic ideas and results of interference experiments related to coherence and decoherence of matter waves and certain post-selection variations, gravitationally induced quantum phase shifts, Berry's geometrical phases, spinor symmetry and spin superposition, and Bell's inequalities are all discussed and explained in this book. Both the scalar and vector Aharonov-Bohm topological interference effects and the neutron version of the Sagnac effect are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are also topics of this book. It includes the theoretical underpinning as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The observed phase shifts due to the Earth's gravity and rotation indicate a close connection to relativity theory. Neutron interferometry can be considered as a central technique of quantum optics with massive particles. It has stimulated the development of interferometry with atoms, molecules and clusters. The book is written in a style that will be suitable at the senior undergraduate and beginning of graduate level. It will interest and excite many students and researchers in neutron, nuclear, quantum, gravitational, optical, and atomic physics. Lecturers teaching courses in modern physics and quantum mechanics will find a number of interesting and historic experiments they may want to include in their lectures.