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CRC Press eBooks

A Quantum Mechanics Primer

Supriyo Bandyopadhyay, Marc Cahay

Published Mar 20, 2008• 0 citations
Publisher

Abstract

This chapter should be treated as an appendix. It is included for completeness and covers certain fundamentals of Quantum Mechanics that will aid the understanding of topics discussed in this textbook. The reader is urged to refer to many of the good introductory textbooks on the subject to learn or revisit the fundamental concepts [1, 2, 3, 4].

DOI
10.1201/9781420004748-18

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This chapter should be treated as an appendix. It is included for completeness and covers certain fundamentals of Quantum Mechanics that will aid the understanding of topics discussed in this textbook. The reader is urged to refer to many of the good introductory textbooks on the subject to learn or revisit the fundamental concepts [1, 2, 3, 4].
This chapter should be treated as an appendix. It is included for completeness and covers certain fundamentals of quantum mechanics that will aid the understanding of topics discussed in this textbook. The reader is urged to refer to many of the good introductory textbooks on the subject to learn or revisit the fundamental concepts [1, 2, 3, 4]. First, we briefly discuss three key ingredients of quantum mechanics, i.e., the blackbody radiation spectrum, the concept of the photon and de Broglie wavelength, and the related wave-particle duality concept. Next, we briefly restate the four major postulates of quantum mechanics used in the so-called orthodox or Copenhagen interpretation of quantum mechanics that is in vogue. We continue on to describe a generalized form of the Heisenberg Uncertainty Principle which is illustrated with a few familiar bound state problems (particle-in-a-box and one-dimensional harmonic oscillator) and a few spin related problems.
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
An introductory textbook for advanced students of physics, chemistry and computer science, covering an area of physics that has lately witnessed rapid expansion. The topics treated here include quantum information, quantum communication, quantum computing, teleportation and hidden parameters, thus imparting not only a well-founded understanding of quantum theory as such, but also a solid basis of knowledge from which readers can follow the rapid development of the topic or delve deeper into a more specialized branch of research. Commented recommendations for further reading as well as end-of-chapter problems help the reader to quickly access the theoretical basics of future key technologies