Advanced Quantum Mechanics

Author: Ni Guangjiong / et al.
Editor-in-Chief: Gong Shaoming
Publisher:
Publish Date: 2001-06-01
Features: Based on the author's teaching experience and research achievements, this book comprehensively summarizes and analyzes the content of advanced quantum mechanics and its related mathematical methods. The author then organizes a logical system that is easy for readers to understand. Initially written as a lecture note in 1981, the book was refined through continuous teaching and revision, resulting in this final version. The book is divided into ten chapters, covering fundamental concepts and methods in quantum mechanics, quantum scattering theory, symmetry and angular momentum theory in quantum mechanics, quantization of electromagnetic fields and their interaction with charged particles, density matrix and quantum statistics, phase in quantum mechanics, motion of electrons in magnetic fields, methods and applications of quantum many-body problems, relativistic quantum mechanics, and an experimental perspective on the fundamental interpretation of quantum mechanics. Many contents of the book, such as Levinson's theorem, geometric phase, Casimir effect, fractional statistics, the essence of special relativity, and the fundamental interpretation of quantum mechanics, reflect the author's specialized research achievements. This book can serve as a textbook for graduate students in physics and a reference for advanced students. It is also a valuable reference for researchers in related fields. It will help you pass through the gate of quantum mechanics and enter your respective cutting-edge research areas.
Excerpt: For every quantum mechanics problem he encountered, he would provide an answer. But when I asked him which problem he found most fascinating, he couldn't articulate one. To him, the entire field of quantum mechanics seemed vast and indistinct. My perspective on his view is this: despite absorbing a great deal of information, he had not developed a sense of taste. This is the fundamental reason why I cannot adopt an optimistic attitude toward his future development. Learning a subject is not just about acquiring knowledge and special techniques; it is also about understanding its significance and appreciating its essence. If, after studying quantum mechanics, one does not recognize what is important, what is beautiful, or what is worth debating passionately and persistently, then I believe they have not truly absorbed the subject. They have only learned knowledge that can help them score well on exams, which is not the spirit of true scholarship. They have failed to grasp the fundamental value of the problems they study. Learning a discipline, whether physics or otherwise, is not just about mastering its knowledge, theorems, and axioms; it is also about understanding the meaning, spirit, and importance of these knowledge, theorems, and axioms. Only when you perceive their significance to a certain degree can you truly internalize them. I believe that a mature and well-read student, if exposed to some suitable or important articles early in their studies and absorbs their spirit, will greatly benefit in choosing the right problems and methods to solve them.
1.1 Spin-1/2 Systems
1.1A Electron Spin
Long-term research on atomic and molecular processes has gradually revealed that understanding a state in the microscopic world is quite different from describing macroscopic states. The system that exemplifies this characteristic is the electron's spin. At first glance, it seems to have no classical counterpart.