This book offers readers an entirely original and unconventional view of quantum mechanics. It is a view that accepts quantum mechanics as the natural way to think about the way nature works, rather than the view commonly expressed, especially in books on quantum physics, that quantum theory is weird and counterintuitive. It is based on the concept of itemization. From this simple premise, quantities like energy and momentum, both linear and angular emerge naturally, as do configuration space, potentials, the electromagnetic field, many-body dynamics, special relativity and relativistic wave mechanics. The many-body dynamics, because it is not tied to physics from the outset, can be applied to population dynamics outside physics as well as the usual physical situations. From this emerges much of the basic physics that describes, mathematically, how the natural world behaves. This accessible introduction does not require exotic maths, and is aimed at inquisitive physics students and professionals who are interested in exploring unconventional approaches to physics. It may also be of interest to anyone studying quantum information theory or quantum computing. Key Features Provides a unique, new approach to understanding quantum mechanics. Uses basic concepts and mathematical methods accessible at the undergraduate level. Presents applications outside physics, including a newly devised and original model of cell division that shows how cancer-cell population explosions occur. "What [the author] has done is changed the way of thinking about how to organize the foundations of quantum mechanics and the approach is a very natural one. This is a book that has the potential to be quite an important one in how we understand the origins of the quantum theory.This is not an ordinary quantum textbook. It is not trying to teach the full curriculum. It is instead focused on showing the origins of quantum mechanics and how it fits into the relativistic and quantum field theory worlds. It is more in line with foundations of quantum mechanics books, but in my opinion, way better than the whole lot of the rest of them. There is no comparison."— Professor James Freericks, Georgetown University.
This book offers readers an entirely original and unconventional view of quantum mechanics. It is a view that accepts quantum mechanics as the natural way to think about the way nature works, rather than the view commonly expressed, especially in books on quantum physics, that quantum theory is weird and counterintuitive. It is based on the concept of itemization. From this simple premise, quantities like energy and momentum, both linear and angular emerge naturally, as do configuration space, potentials, the electromagnetic field, many-body dynamics, special relativity and relativistic wave mechanics. The many-body dynamics, because it is not tied to physics from the outset, can be applied to population dynamics outside physics as well as the usual physical situations. From this emerges much of the basic physics that describes, mathematically, how the natural world behaves. This accessible introduction does not require exotic maths, and is aimed at inquisitive physics students and professionals who are interested in exploring unconventional approaches to physics. It may also be of interest to anyone studying quantum information theory or quantum computing. Key Features Provides a unique, new approach to understanding quantum mechanics. Uses basic concepts and mathematical methods accessible at the undergraduate level. Presents applications outside physics, including a newly devised and original model of cell division that shows how cancer-cell population explosions occur. "What [the author] has done is changed the way of thinking about how to organize the foundations of quantum mechanics and the approach is a very natural one. This is a book that has the potential to be quite an important one in how we understand the origins of the quantum theory.This is not an ordinary quantum textbook. It is not trying to teach the full curriculum. It is instead focused on showing the origins of quantum mechanics and how it fits into the relativistic and quantum field theory worlds. It is more in line with foundations of quantum mechanics books, but in my opinion, way better than the whole lot of the rest of them. There is no comparison."— Professor James Freericks, Georgetown University.
Introduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics. It provides an accessible treatment of how to use quantum mechanics and why it is so successful in explaining natural phenomena. This book clarifies various aspects of quantum physics such as ‘why quantum mechanics equations contain “I”, the imaginary number?’, ‘Is it possible to make a transition from classical mechanics to quantum physics without using postulates?’ and ‘What is the origin of the uncertainty principle?’. A significant proportion of discussion is dedicated to the issue of why the wave function must be complex to properly describe our “real” world. The book also addresses the different formulations of quantum mechanics. A relatively simple introductory treatment is given for the “standard” Heisenberg matrix formulation and Schrodinger wave-function formulation and Feynman path integrals and second quantization are then discussed. This book will appeal to first- and second-year university students in physics, mathematics, engineering and other sciences studying quantum mechanics who will find material and clarifications not easily found in other textbooks. It will also appeal to self-taught readers with a genuine interest in modern physics who are willing to examine the mathematics and physics in a simple but rigorous way. Key Features: Written in an engaging and approachable manner, with fully explained mathematics and physics concepts Suitable as a companion to all introductory quantum mechanics textbooks Accessible to a general audience
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
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.
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.
The proposed book consists of two parts and is devoted to the systematic analysis of quantum mechanics and the modern theory of electromagnetic phenomena. Some inaccuracies of the application of mathematics in theoretical physics are discussed. This first part examines in detail the basic concepts of quantum mechanics, its apparatus, methods and applications and demonstrates their groundlessness, and often the internal inconsistency of the most common version of the Copenhagen interpretation of quantum mechanics. The book contains a critical analysis of the experiments underlying this theory. All this together proves that the generally accepted version of quantum mechanics is a temporary construction, and the creation of a new consistent theory of the microcosm is required. The book also discusses some alternative ideas applicable to the microcosm. This book may be useful for students, postgraduates, teachers, scientific and technical workers and anyone interested in the basics of physics. To the English version of the book. This is an English translation of the Russian version of the book. Quotations were also translated from Russian-language publications (therefore, for English-language works they are not a literal original, but they convey the essence of the quotations). However, references to pages or chapters have been corrected for the indicated English-language sources.
Scientists have been debating the meaning of quantum mechanics for more than a century. This book for graduate students and researchers gets to the root of the problem: how the contextual nature of empirical truth and the laws of observation impact on our understanding of quantum physics. Bridging the gap between non-relativistic quantum mechanics and quantum field theory, this novel approach to quantum mechanics extends the standard formalism to cover the observer and their apparatus. The author demystifies some of the aspects of quantum mechanics that have traditionally been regarded as extraordinary, such as wave-particle duality and quantum superposition, emphasizing the scientific principles rather than the mathematical modelling. Including key experiments and worked examples throughout, the author encourages the reader to focus on empirically sound concepts and avoid metaphysical speculation. Originally released in 2017, this title has been reissued as an Open Access publication on Cambridge Core.