This book is a collection of lecture notes discussing the basic features of the Quantum Mechanics of Infinite Systems such as collective phenomena, spontaneous symmetry breaking, etc. The mathematical precision has been reduced to a minimum in order to communicate the main ideas to a larger audience including those who are not mathematically meinded. It is aimed at helping students who have difficulty in finding accessible and compact expositions of the material in standard textbooks.
This book is a collection of lecture notes discussing the basic features of the Quantum Mechanics of Infinite Systems such as collective phenomena, spontaneous symmetry breaking, etc. The mathematical precision has been reduced to a minimum in order to communicate the main ideas to a larger audience including those who are not mathematically meinded. It is aimed at helping students who have difficulty in finding accessible and compact expositions of the material in standard textbooks.
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.
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.
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 represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to specific applications. The formulation of quantum theory is explained and supported with illustrations of the general concepts of elementary quantum systems. In addition to traditional topics of nonrelativistic quantum mechanics - including single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, and the theory of angular momentum - the book also covers modern issues, among them quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is also outlined in explanatory notes. Ideal as a supplement to classroom lectures, the book can also serve as a compact and comprehensible refresher of elementary quantum theory for more advanced students.
This modern textbook offers an introduction to Quantum Mechanics as a theory that underlies the world around us, from atoms and molecules to materials, lasers, and other applications. The main features of the book are: * Emphasis on the key principles with minimal mathematical formalism * Demystifying discussions of the basic features of quantum systems, using dimensional analysis and order-of-magnitude estimates to develop intuition * Comprehensive overview of the key concepts of quantum chemistry and the electronic structure of solids * Extensive discussion of the basic processes and applications of light-matter interactions * Online supplement with advanced theory, multiple-choice quizzes, etc.
There is a huge number of excellent and comprehensive textbooks on quantum mechanics. They mainly differ for the approach, more or less oriented to the formalism rather than to the phenomenology, as well as for the topics covered. These lectures have been based mainly on the classical textbook by Gasiorowicz (1974). I must confess that the main reason for my choice of Gasiorowicz (1974) is affective, as it was the textbook where I first learned the basic principles of quantum mechanics. Beyond my personal taste, I now recognize that Gasiorowicz (1974) is still a very good textbook on quantum mechanics, with a rigorous theoretical approach accompanied by a wide collection of applications. If the textbook by Gasiorowicz was my main basis, I have taken much also from other textbooks such as Phillips (2003), as well as from the excellent classical textbook by Dirac (1981). In order to avoid complications in the mathematics and in the notation, the topic is presented in these notes with reference to one-dimensional systems, with just a few marginal extensions to the three-dimensional formulation.