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CRC Press eBooks

Visualizing Quantum Mechanics with Python

Steve Spicklemire

Published Apr 10, 2024• 0 citations
Publisher

Abstract

Quantum Mechanics can be an abstract and complex subject. Students often complain of confusion, struggle, and frustration as they try to master the topic. The goal of this book is to reduce the complexity and clarify the abstractions with concrete visual examples driven by simple python programs. It is assumed that the reader is concurrently taking a course in quantum mechanics, or self-studying quantum mechanics, but is looking for supplementary material to help with understanding and visualizing how quantum mechanics works. The focus of this book is writing python programs to visualize the underlying behavior of the mathematical theory. The background needed to understand quantum mechanics is differential equations, linear algebra and modern physics. We need a strong foundation in differential equations and linear algebra because the behavior of quantum systems is governed by equations that are written in terms of these concepts. Modern physics includes concepts such as special relativity and quantum phenomena like the photoelectric effect and energy quantization that the theory of quantum mechanics seeks to explain. This book is also not an introduction to the python programming language, or to numpy, or even to VPython. However its programming examples start simply and grow more complex as the chapters progress, so deep expertise in any of these is not a pre-requisite. Key features: · Provides an accessible and practical guide to the abstractions in quantum mechanics with concrete visual examples driven by simple python programs. · Contains few derivations, equations, and proofs. · For complete beginners of python programming, appendix B serves as a very brief introduction to the main concepts needed to understand the code in this book.

DOI
10.1201/9781003437703

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Quantum Mechanics can be an abstract and complex subject. Students often complain of confusion, struggle, and frustration as they try to master the topic. The goal of this book is to reduce the complexity and clarify the abstractions with concrete visual examples driven by simple python programs. It is assumed that the reader is concurrently taking a course in quantum mechanics, or self-studying quantum mechanics, but is looking for supplementary material to help with understanding and visualizing how quantum mechanics works. The focus of this book is writing python programs to visualize the underlying behavior of the mathematical theory. The background needed to understand quantum mechanics is differential equations, linear algebra and modern physics. We need a strong foundation in differential equations and linear algebra because the behavior of quantum systems is governed by equations that are written in terms of these concepts. Modern physics includes concepts such as special relativity and quantum phenomena like the photoelectric effect and energy quantization that the theory of quantum mechanics seeks to explain. This book is also not an introduction to the python programming language, or to numpy, or even to VPython. However its programming examples start simply and grow more complex as the chapters progress, so deep expertise in any of these is not a pre-requisite. Key features: · Provides an accessible and practical guide to the abstractions in quantum mechanics with concrete visual examples driven by simple python programs. · Contains few derivations, equations, and proofs. · For complete beginners of python programming, appendix B serves as a very brief introduction to the main concepts needed to understand the code in this book.
Q UANTUM MECHANICS can be an abstract and complex subject. Students often complain of confusion, struggle, and frustration as they try to master the topic. The goal of this book is to reduce the complexity and clarify the abstractions with concrete visual examples driven by simple python programs. It is assumed that the reader is concurrently taking a course in quantum mechanics, or self-studying quantum mechanics, but is looking for supplementary material to help with understanding and visualizing how quantum mechanics works. There are few derivations, equations, or proofs. Those are left to the more formal textbooks and lectures. The focus of this book is writing python programs to visualize the underlying behavior of the mathematical theory. The background needed to understand quantum mechanics is differential equations, linear algebra and modern physics. We need a strong foundation in differential equations and linear algebra because the behavior of quantum systems is governed by equations that are written in terms of these concepts. Modern physics includes concepts such as special relativity and quantum phenomena like the photoelectric effect and energy quantization that the theory of quantum mechanics seeks to explain. This book is also not an introduction to the python programming language, or to numpy, or even to VPython. Having said that, the programming examples will start simply and grow more complex as the story line progresses, so deep expertise in any of these is not a pre-requisite. If you're completely new to python programming, appendix B has been provided as a very brief introduction to the main concepts needed to understand the code in this book.
This book provides an easy-to-read but practical introduction to quantum gate simulation to serious learners of the subject. Fundamental physical concepts and selected programming examples of quantum simulations are described for readers who want to use the simulation with a physical understanding background without the use of rigorous mathematics. This book is intended to offer a self-study book for senior and graduate students of physics, computer science, and mathematics who want to learn and write quantum codes. It may also serve as a textbook or a reference in academia and industry. Readers are expected to have introductory knowledge of linear algebra although it is briefly reviewed in this book. Some experience of computer programming is helpful, but no prior knowledge of Python is required for writing the quantum codes shown in this book. Part of IOP Series in Quantum Technology. Key features • Easy-to-read content for self-paced readers. • Many examples with background physics. • Detailed description of entanglement and teleportation. • Guide to industrial resources. • DIY quantum gate simulations.
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
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
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
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.