Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics. Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China. Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.
Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics. Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China. Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.
Quantum Mechanics is one of the most fundamental and intellectually profound branches of modern physics. It provides the theoretical framework for understanding the behavior of matter and energy at atomic and subatomic scales and forms the basis for numerous advancements in science and technology, including semiconductor devices, lasers, nanotechnology, quantum computing, and quantum communication. Despite its abstract nature, quantum mechanics remains indispensable for explaining physical phenomena that cannot be addressed by classical physics. This book, Quantum Mechanics, has been written with the primary objective of presenting the subject in a clear, logical, and student-friendly manner, while maintaining the necessary mathematical rigor and conceptual depth. The text is designed to bridge the gap between classical physics and quantum theory, guiding readers through the evolution of ideas that led to the development of quantum mechanics and its modern interpretations. The book begins with an introduction to the historical background and foundational principles of quantum theory, highlighting the limitations of classical mechanics and the emergence of quantum concepts such as wave–particle duality and quantization. It then systematically develops the mathematical framework of quantum mechanics, including the Schrödinger equation, wave functions, operators, eigenvalue problems, and measurement theory. Key quantum systems and applications are discussed with careful attention to physical interpretation and problem-solving strategies. Special emphasis has been placed on clarity of explanation, step-by-step derivations, and the use of illustrative examples to help students develop a strong conceptual understanding. Each chapter is organized in a structured manner to support effective learning and includes solved problems and exercises that reinforce theoretical concepts and analytical skills. This book is intended for undergraduate and postgraduate students of physics, engineering, and allied disciplines, and it will also serve as a useful reference for educators and researchers. The content has been aligned with standard university curricula and is suitable for both classroom instruction and self-study. It is the author’s sincere hope that this book will make the study of quantum mechanics more accessible and intellectually rewarding, encouraging readers to develop a deeper appreciation for the quantum nature of the physical world. Constructive feedback and suggestions from readers are welcome and will be valuable for improving future editions of this book.
This book presents an accessible treatment of non-relativistic and relativistic quantum mechanics. It is an ideal textbook for undergraduate and graduate physics students, and is also useful to researchers in theoretical physics, quantum mechanics, condensed matter, mathematical physics, quantum chemistry, and electronics. This student-friendly and self-contained textbook covers the typical topics in a core undergraduate program, as well as more advanced, graduate-level topics with an elegant mathematical rigor, contemporary style, and rejuvenated approach. It balances theory and worked examples, which reinforces readers' understanding of fundamental concepts. The analytical methods employed in this book describe physical situations with mathematical rigor and in-depth clarity, emphasizing the essential understanding of the subject matter without need for prior knowledge of classical mechanics, electromagnetic theory, atomic structure, or differential equations. Key Features: • Remains accessible but incorporates a rigorous, updated mathematical treatment• Laid out in a student-friendly structure• Balances theory with its application through examples Lukong Cornelius Fai is a professor of theoretical physics at the Department of Physics, Faculty of Sciences, University of Dschang, Cameroon. He is Head of Condensed Matter and Nanomaterials as well as the Mesoscopic and Multilayer Structures Laboratory. He was formerly a senior associate at the Abdus Salam International Centre for Theoretical Physics (ICTP), Italy. He holds a Master of Science in Physics and Mathematics (1991) as well as a Doctor of Science in Physics and Mathematics (1997) from Moldova State University. He is the author of over 170 scientific publications and five textbooks.
Concepts of QUANTUM MECHANICS is one of the most fundamental and intellectually profound branches of modern physics. It provides the theoretical framework for understanding the behavior of matter and energy at atomic and subatomic scales and forms the basis for numerous advancements in science and technology, including semiconductor devices, lasers, nanotechnology, quantum computing, and quantum communication. Despite its abstract nature, concepts of QUANTUM MECHANICS remains indispensable for explaining physical phenomena that cannot be addressed by classical physics. This book, Concepts of QUANTUM MECHANICS, has been written with the primary objective of presenting the subject in a clear, logical, and student-friendly manner, while maintaining the necessary mathematical rigor and conceptual depth. The text is designed to bridge the gap between classical physics and quantum theory, guiding readers through the evolution of ideas that led to the development of concepts of QUANTUM MECHANICS and its modern interpretations. The book begins with an introduction to the historical background and foundational principles of quantum theory, highlighting the limitations of classical mechanics and the emergence of quantum concepts such as wave–particle duality and quantization. It then systematically develops the mathematical framework of concepts of QUANTUM MECHANICS, including the Schrödinger equation, wave functions, operators, eigenvalue problems, and measurement theory. Key quantum systems and applications are discussed with careful attention to physical interpretation and problem-solving strategies. Special emphasis has been placed on clarity of explanation, step-by-step derivations, and the use of illustrative examples to help students develop a strong conceptual understanding. Each chapter is organized in a structured manner to support effective learning and includes solved problems and exercises that reinforce theoretical concepts and analytical skills. This book is intended for undergraduate and postgraduate students of physics, engineering, and allied disciplines, and it will also serve as a useful reference for educators and researchers. The content has been aligned with standard university curricula and is suitable for both classroom instruction and self-study. It is the author’s sincere hope that this book will make the study of concepts of QUANTUM MECHANICS more accessible and intellectually rewarding, encouraging readers to develop a deeper appreciation for the quantum nature of the physical world. Constructive feedback and suggestions from readers are welcome and will be valuable for improving future editions of this book.
Over the course of the past two to three decades, new tools of presentation and mathematical treatment have emerged and the subject matter of quantum mechanics has gone through significant changes. A Textbook on Modern Quantum Mechanics presents the selected elementary, intermediate, and advance topics with rejuvenated approach to the subject matter. Newly merged topics from contemporary physics and chemistry are included in the text as well as solved examples. The book covers: (i) fundamental discoveries that are the foundation of modern quantum mechanics; (ii) solution of Schrödinger’s wave equation for 1D problems and their importance; (iii) matrix and vector formulation of quantum mechanics; (iv) transformations, symmetries, and conservation laws; (v) angular and spin momenta; (vi) solution of Schrödinger equation for central potentials; (vii) time-independent perturbation theory, variational method and WKB approximation; (viii) quantum theory of scattering; (xi) many-particle systems and their quantum mechanical treatments; (x) time-dependent perturbations and the interaction of fields with matter; (xi) relativistic quantum mechanics; and (xii) quantization of fields and the second quantization. Key Features: It provides everything a student needs to know for succeeding at all levels of the undergraduate and graduate studies. It covers most of the topics that are taught under (a) elementary, (b) intermediate, and (c) advance courses of quantum mechanics at universities and colleges. It has detailed and elegant mathematical treatment with contemporary style of interpretation and presentation in simple English. Solved examples and unsolved exercises that are part of each chapter to consolidate the readers' understanding of fundamental concepts. The subject matter of the book is well tested on the students taught by the author over a period of 30 years. This is a valuable textbook for students pursuing Bachelor of Science, Master of Science, and Doctor of Philosophy (PhD) degrees in the subjects of Physics, Chemistry, and materials science in India, South Asian countries, the United States, and Europe.
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.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.