Quantum Mechanics

Quantum mechanics: from classical analytical mechanics to quantum mechanics, simulation, foundations & engineering

Quantum mechanics is a fundamental subject in physics, often considered to be one of the most conceptually challenging topics. In many undergraduate courses, it is assumed that students are unfamiliar with the Lagrangian and Hamiltonian formulations of classical mechanics or the role of probability in Liouville's theorem (analytical mechanics). As a result, quantum physics is typically introduced using heuristic arguments, which can lead to surprising and counterintuitive concepts, and sometimes even incorrect interpretations.

This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By introducing and utilising classical mechanics, we provide a solid foundation for understanding quantum phenomena. We discuss important examples within this context and explore both exact and computational methods.

Additionally, this book delves into quantum measurement and the transition from the quantum to the classical realm. It also introduces the emerging field of Quantum Systems Engineering, which focuses on the systematic design and construction of quantum technologies, such as quantum computers and sensors.

Key features of this textbook include:

• Mathematics and Classical Analytical Mechanics: The necessary mathematical background and classical analytical mechanics are introduced gradually, allowing readers to focus on one conceptual challenge at a time.
• Deductive Approach: Quantum mechanics is presented on the firm foundation of classical analytical mechanics, ensuring a logical progression of concepts.
• Pedagogical Features: The book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding.
• Comprehensive Coverage: It goes beyond introductory texts by including topics such as open quantum systems and phase-space methods. Advanced computational methods are also discussed, including good programming practices and code design. Much of the code needed to reproduce figures throughout the book is provided.
• Consideration of Foundations: The measurement problem and correspondence principle are addressed only after sufficient material has been introduced to allow for an open and critical discussion.
• Introduction to Quantum Systems Engineering: This book provides an accessible introduction and motivation to this framework.

This textbook is suitable for undergraduate students in physics and graduate students in mathematics, chemistry, engineering, and materials science.

Mark Everitt is the Director of Studies for Physics at Loughborough University, UK, where he has led a comprehensive and innovative revision of the physics degrees, increasing the level of challenge, guided by principles of authenticity and industry requirements. Notably, the first seven chapters of the book are derived from his second-year introductory core Quantum Physics module in these new degrees, which he leads and delivers with Duffus. He has been actively involved in a nationwide review aimed at enhancing the quality assurance and accreditation frameworks for physics degrees in the UK. His research includes the engineering of quantum circuits and devices for quantum technologies, feedback, measurement and control of quantum systems, and pioneering the field of quantum systems engineering as a distinct discipline.

Stephen Duffus is a university teacher within the Physics Department at Loughborough University. He has an established reputation of communicating complex ideas in an engaging and accessible fashion. During his PhD, his main area of research was in open quantum systems.

Kieran Niels Bjergstrom started his career as a theoretical physicist where his research focused on realistic modelling of open quantum systems, the reliability of quantum devices, and early notions of Quantum Systems Engineering – which was the topic of his PhD thesis. He has worked in and out of academia to develop Quantum Systems Engineering principles, tools and methodologies for realising mature quantum technologies with commercial traction. He is director of a technology and strategy consultancy, advising on areas of innovation, including the strategic impact of quantum technologies, methods and policies for realising quantum technology's commercial potential, and applied quantum systems engineering.

Chapter 1. Mathematical Preliminaries

Chapter 2. Notes on Classical Mechanics

Chapter 3. The Schrödinger View/Picture

Chapter 4. Other Formulations of Quantum Mechanics

Chapter 5. Vectors and Angular Momentum

Chapter 6. Some Analytic and Semi-Analytic Methods

Chapter 7 Applications and Examples

Chapter 8. Computational Simulation of Quantum Systems

Chapter 9. Open Quantum Systems

Chapter 10. Foundations: Measurement and the Quantum to Classical Transition

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