Xiang T.Building Blocks of Quantum Mechanics.Theory and App 2022

Textbook in PDF format

The object of this textbook is to provide a concise yet comprehensive introduction to the principles, concepts, and methods of quantum mechanics. It covers the basic building blocks of quantum mechanics theory and applications, illuminated throughout by accurate explanation, physical insight, and intelligible examples, so that students can easily focus on. After a brief outline of the innovative ideas that lead up to the quantum theory, the book introduces the Schrodinger equation, theory of representation, physical meaning of wave functions, measurement postulate, uncertainty principles, and the standard quantum formalism, like the physical observables and their expectation values, the Schrodinger and Heisenberg pictures, symmetry and conservation laws, electromagnetic interaction and gauge invariance, angular momentum, adiabatic and diabatic evolutions of quantum states, entanglement and identical particles, and relativistic quantum mechanics. The theory is materialized and enriched by including many typical and heuristic examples of quantum mechanics, such as the one-dimensional eigen-problems, harmonic oscillator, Aharonov-Bohm effect, Landau levels, hydrogen atom, Landau-Zener transition and Berry phase. The approximate methods commonly used in quantum mechanics, such as the WKB approximation, variational principle, stationary and time-dependent perturbation theories, are also introduced.
This book results from an undergraduate course given at the University of Chinese Academy of Sciences. With careful development of concepts and thorough explanations, the book is aimed to make quantum mechanics accessible for students majoring in physics, chemistry or electronic engineering and professionals in mathematics and computer sciences. It is self-contained, suitable for a semester course for both junior and senior students. It is assumed that the reader is reasonably familiar with atomic structure, electromagnetism, differential equations, and linear algebra. It may also serve as a beginner’s reference book for self-studying Quantum Mechanics