QUANTUM MECHANICS

From classical analytical mechanics to quantum mechanics, simulation, foundations & engineering

Quantum mechanics is a fundamental and conceptually challenging area of physics. It is usually assumed that students are unfamiliar with Lagrangian and Hamiltonian formulations of classical mechanics and the role played by probability. As a result, quantum physics is typically introduced using heuristic arguments, obscuring synergies with classical mechanics.

This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By doing so, a solid foundation for understanding quantum phenomena is provided.

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: This book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding.
• Comprehensive Coverage: Including advanced topics such as open quantum systems, phase-space methods, and computational methods for quantum physics including good programming practice and code design. Much of the code needed to reproduce figures throughout this book is included.
• Consideration of Foundations: The measurement problem and correspondence principle are addressed, including an open and critical discussion of their interpretation and consequences.
• Introduction to Quantum Systems Engineering: This is the first book to introduce Quantum Systems Engineering approaches for applied quantum technologies development.

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

The important changes quantum mechanics has undergone in recent years are reflected in this approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with developments in the field. Historical, mathematical and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available at www.cambridge.org/Auletta.

Quantum mechanics is one of the most brilliant and exciting theories of the 20th century. It has not only explained a wide range of phenomena but has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. As quantum mechanics involves the introduction of a new conceptual framework, the new ideas are explicitly mentioned and explained in detail in this book, and wherever possible, the various aspects of original thinking of eminent physicists are reflected. The emphasis is on helping students comprehend the significance of the underlying principles and understand the ways the new concepts were introduced. Including many worked examples and problems, this book will be an invaluable resource for students in physics, chemistry and electrical engineering needing a clear and rigorous introduction to quantum mechanics.

Quantum mechanics is one of the most brilliant and exciting theories of the 20th century. It has not only explained a wide range of phenomena but has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. As quantum mechanics involves the introduction of a new conceptual framework, the new ideas are explicitly mentioned and explained in detail in this book, and wherever possible, the various aspects of original thinking of eminent physicists are reflected. The emphasis is on helping students comprehend the significance of the underlying principles and understand the ways the new concepts were introduced. Including many worked examples and problems, this book will be an invaluable resource for students in physics, chemistry and electrical engineering needing a clear and rigorous introduction to quantum mechanics.

This book introduces notation, terminology, and basic ideas of relativistic quantum theories. The discussion proceeds systematically from the principle of relativity and postulates of quantum logics to the construction of Poincaré invariant few-particle models of interaction and scattering. It is the first of three volumes formulating a consistent relativistic quantum theory of interacting charged particles. 　 Contents Quantum logic Poincaré group Quantum mechanics and relativity Observables Elementary particles Interaction Scattering Delta function Groups and vector spaces Group of rotations Lie groups and Lie algebras Hilbert space Operators Subspaces and projections Representations of groups and algebras Pseudo-orthogonal representation of Lorentz group