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.
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.
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.
Based on years of teaching experience, this book provides a clearly structured and accessible introduction to the fundamental principles of quantum mechanics, tailored for undergraduate students. The text builds a strong conceptual and mathematical foundation while promoting intuitive understanding and critical thinking. Students progress from basic concepts such as wave mechanics to more advanced topics within matrix mechanics. Complex concepts are presented in a diligent and understandable way, achieving a balance between conceptual insight and mathematical rigor without oversimplifying the subject. Thoroughly class-tested, this book is designed to support both classroom instruction and independent study. It will serve as a great tool for undergraduates studying introductory and intermediate quantum mechanics, as well as modern physics and quantum systems for engineers.
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.
Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.
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.
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.