Advanced Quantum Mechanics: The Classical-quantum Connection

This book provides a coherent introduction to Gutzwiller's trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, calculus, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, physics, and engineering, this book is attractive for professional scientists and engineers as well.

Following a thorough review of elementary concepts in classical and quantum mechanics, the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller's approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman's Path Integrals. Numerous applications, including the exact solutions of "unsolvable" one-dimensional quantum problems, illustrate the power of Gutzwiller's method. Worked examples throughout the text illustrate the material and provide immediate hands-on demonstrations of tools and concepts.

KEY FEATURES

Simultaneously develops both classical and quantum mechanics, emphasizing the classical-quantum connection, Contains introductory chapters on classical chaos and quantum mechanics, Includes a section on Feynman's Path Integrals accessible to undergraduate students, Contains an application chapter on exact periodic-orbit solutions of quantum graphs, the standard model of quantum complexity, Places emphasis on cases where Gutzwiller's trace formula yields exact results, Includes exercises at the end of each section and chapter to test the students' mastery of the material, Instructor resources include solutions to the exercises