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Introduction to the Physics of Matter
This book offers an up-to-date, compact presentation of basic topics in the physics of matter, from atoms to molecules to solids, including elements of statistical mechanics. The adiabatic separation of the motion of electrons and nuclei in matter and its spectroscopic implications are outlined for molecules and recalled regularly in the study of the dynamics of gases and solids. Numerous experiments are described and more than 160 figures give a clear visual impression of the main concepts. Sufficient detail of mathematical derivations is provided to enable students to follow easily. The focus is on present-day understanding and especially on phenomena fitting various independent-particle models. The historical development of this understanding, and phenomena such as magnetism and superconductivity, where interparticle interactions and nonadiabatic effects play a crucial role, are mostly omitted. A final outlook section stimulates the curiosity of the reader to pursue the study of such advanced topics in graduate courses.
Introductory Quantum Mechanics
This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.
Probability and Stochastic Processes for Physicists
This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffus...
Quantum Physics of Light and Matter
This compact but exhaustive textbook, now in its significantly revised and expanded second edition, provides an essential introduction to the field quantization of light and matter with applications to atomic physics and strongly correlated systems. Following an initial review of the origins of special relativity and quantum mechanics, individual chapters are devoted to the second quantization of the electromagnetic field and the consequences of light field quantization for the description of electromagnetic transitions. The spin of the electron is then analyzed, with particular attention to its derivation from the Dirac equation. Subsequent topics include the effects of external electric an...
General Relativity and Gravitational Waves
This book serves as a textbook for senior undergraduate students who are learning the subject of general relativity and gravitational waves for the first time. Both authors have been teaching the course in various forms for a few decades and have designed the book as a one stop book at basic level including derivations and exercises. A spectacular prediction of general relativity is gravitational waves. Gravitational waves were first detected by the LIGO detectors in 2015, hundred years after their prediction. Both authors are part of the LIGO Science Collaboration and were authors on the discovery paper. Therefore, a strong motivation for this book is to provide the essential concepts of ge...
A Mathematical Primer on Quantum Mechanics
This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
A Primer on Hilbert Space Theory
This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between fu...
Fundamentals of Friction and Wear on the Nanoscale
This book provides an updated review on the development of scanning probe microscopy and related techniques, and the availability of computational techniques not even imaginable a few decades ago. The 36 chapters cover instrumental aspects, theoretical models and selected experimental results, thus offering a broad panoramic view on fundamental issues in nanotribology which are currently being investigated. Compared to the first edition, several topics have been added, including triboluminescence, graphene mechanics, friction and wear in liquid environments, capillary condensation, and multiscale friction modeling. Particular care has been taken to avoid overlaps and guarantee the independence of the chapters. In this way, our book aims to become a key reference on this subject for the next five to ten years to come.
