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
Table of Contents
Electromagnetic radiation behaving as particle. Blackbody Radiation. The Photoelectric effect. X-Rays. Particles behaving as wave: concept of matter waves. De Broglie’s matter waves. Double-slit Experiment. Heisenberg’s Uncertainty Principle. Measurement and Observation. Wave Mechanics: Schrodinger’s wave equation of a particle. The Schrodinger equation. Stationary states. Expectation values, Uncertainties and operators. Particle-Wave propagation (wavepacket, phase and group velocities). Differences between quantum mechanics and classical mechanics. Wave Mechanics: Schrodinger’s wave equation of a particle- II. Particle in a box-The infinite square well. The finite square well. The free-particle. The potential step. The potential barrier and tunneling. Matrix Mechanics: Formalism. Matrix Algebra. Transformation theory. Matrix theory of the harmonic oscillator. Equation of motion using matrix mechanics. Differences between matrix mechanics and wave equation approaches. Quantum Mechanics in Three Dimensions and the Hydrogen Atom. The Schrodinger Equation in Three Dimensions. The 3D Infinite well. Energy Quantization and Spectral Lines in Hydrogen Atom. The Schrodinger Equation for a Central Force. Quantum Mechanics in three dimensions – II. Applications of Quantum Mechanics
Dr. Shabnam Siddiqui is a research assistant professor at Louisiana Tech University, LA. She teaches physics and conducts research for developing electrochemical microsensors using carbon nanomaterials. She applies active learning approaches for teaching physics courses and focuses on developing new methods for learning physics, and quantum mechanics. Dr. Siddiqui studies properties of carbon nanomaterials for attaining reliable and real-time sensing. She has authored over 20 peer reviewed journal papers. She earned a PhD in physics in quantum computing and quantum information in 2006 from the University of Arkansas at Fayetteville, AR. Dr. Siddiqui received postdoctoral training at NASA Ames Research Center, CA, and the University of Pittsburgh, PA. She had also worked at Advanced Diamond Technologies, IL prior to joining Louisiana Tech.