Quantum mechanics to a large extent is a subject which conceptually is abstract and very mathematical in nature. Despite its abstract formalism it has proved to be a storehouse of ideas of enormous practical value. These radically new ideas, boldly proposed and strikingly uncommon, have helped to unlock deep secrets of the world, especially at the microscopic level where the breakdown of classical physics becomes rather apparent. There flows indeed from this subject a vast stream of concrete, everyday life applications. The phenomenon of transistors, television, semiconductors, computers, lasers, to name a few, instruments of unde-bated importance for communication, education, energy requirements, medicine, etc.—all involve quantum mechanical effects. The work of P. Lenard and especially of A. Einstein on the photoelectric effect, for example, helped toward the development of television. Our world has been positively changed by the fruits of this elegant subject and its forward thinking founders.
Quantum mechanics to a large extent is a subject which conceptually is abstract and very mathematical in nature. Despite its abstract formalism it has proved to be a storehouse of ideas of enormous practical value. These radically new ideas, boldly proposed and strikingly uncommon, have helped to unlock deep secrets of the world, especially at the microscopic level where the breakdown of classical physics becomes rather apparent. There flows indeed from this subject a vast stream of concrete, everyday life applications. The phenomenon of transistors, television, semiconductors, computers, lasers, to name a few, instruments of unde-bated importance for communication, education, energy requirements, medicine, etc.—all involve quantum mechanical effects. The work of P. Lenard and especially of A. Einstein on the photoelectric effect, for example, helped toward the development of television. Our world has been positively changed by the fruits of this elegant subject and its forward thinking founders.
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
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
It is now generally accepted that quantum mechanics occupies a central place in microscopic physical theory. The importance of this discipline shows up in the research journals, and also in the graduate physics curriculum. Not only is quantum mechanics a required subject, both for experimental and theoretical students; it appears as well to be influencing the way in which classical physics is taught. Presentations of classical mechanics that slight the traditional problems of planetary motion, unsymmetrical tops and dissipative systems in favor of collision theory and Poisson brackets are becoming more and more prevalent. With the much younger subject of classical electrodynamics, the analogous tendency is less marked, although here again emphasis is being placed on those examples that bring the student closest to the formalism of quantum electrodynamics. Such trends are of course proper and reasonable, especially so long as no important classical ideas are omitted from consideration. Indeed, the study of acoustics, hydrodynamics, and elasticity probably benefits from an early introduction of field concepts.
Quantum mechanics occupies a unique position in the history of science. It has survived all experimental tests to date, culminating with the most precise comparison of any measurement to any theory – a 1987 measurement of the electron's magnetic moment, or gyromagnetic ratio g e = 2.002 319 304 39 (Van Dyck et al. 1987), agreeing with QED theory to 12 digits. Despite this and other dramatic successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties in reconciling quantum physics with the classical laws of physics that govern macroscopic bodies. If quantum mechanics is indeed a complete theory of nature, why does it not apply to everyday life? Even Richard Feynman (1982), a fierce defender of quantum mechanics, memorably stated that: We have always had a great deal of difficulty in understanding the world view that quantum mechanics represents … Okay, I still get nervous with it … It has not yet become obvious to me that there is no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. In the dawn of the twenty-first century, John A. Wheeler's big question “Why the quantum?” has returned to the forefront of physics with full steam. Advances in experimental physics are beginning to realize the same thought-experiments that proved helpful to Einstein, Bohr, Heisenberg, Schrödinger, and the other founders of quantum mechanics.
Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary classical physics concepts) and then introduces the fundamentals of quantum mechanics, including the wave function, superposition, entanglement, Bell's theorem, etc., and applications to Bose--Einstein condensation, quantum computing, and much more. The interpretation of the mathematics of quantum mechanics into a world view has been the subject of much controversy. The result is a variety of conflicting interpretations, from the famous Copenhagen view of Bohr to the multiple universes of Everett. We discuss these interpretations in the chapter "What is a wave function?" and include some very recent advances, for example, quantum Bayesianism, and measurements of the reality of the wave function.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.