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This quantum mechanics primer will accompany the reader from school to university. The formal basis of the subject is briefly introduced, and the reader is then quickly given the tools to start solving problems as diverse as quantising motion in potentials, quantum mechanical tunnelling, muon catalysed fusion, pair production, motion in nanostructures, and the interference of particles as waves. Chapters 1-3 guide the transition from school to university, and develop the skills and understanding that are typically tested in admissions to university physics, maths and engineering degrees. Chapters 2-5 cover university-level quantum mechanics courses, up to the second year of a typical physics degree. All problems can be answered and marked on the Isaac Physics online platform. Registration is free and gives both students and teachers personalised support through a sophisticated online marking system for all problems. This second edition is a co-publication between Periphyseos Press and Cambridge University Press.
A leisurely but mathematically honest presentation of quantum mechanics for graduate students in mathematics with an interest in physics.
Chapter 1 revises maths and mechanics from the final two school years that are needed to start quantum mechanics. Then chapters 2-5 use these skills, and a little more maths that is later introduced, to explore quantum phenomena through solving problems.
Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.
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.
Introductory text examines classical quantum bead on a track: state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; bead in spherical shell. 1992 edition.
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
This book provides a comprehensive introduction to quantum mechanics, supported by numerous solved exercises. Aiming to be both exhaustive and educational, it minimises overly formal aspects by presenting the wave mechanical approach to quantum mechanics. The book simplifies and rigorously covers a large set of fundamental topics such as potential wells and barriers, wave packets, harmonic oscillators, and the hydrogen atom. It also addresses spin and, in simple terms, the conceptual difficulties of quantum physics and Bell’s inequalities. The discussion extends to relativistic quantum mechanics. Each chapter includes exercises designed to test comprehension and facilitate optimal assimilation of the material, and are followed by detailed solutions. Intended for both personal study and course support, this book is valuable for anyone curious about the subject. However, it is specifically targeted at undergraduate and master’s students in physics, chemistry, and mathematics, as well as engineering students.