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, 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 just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
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For Advanced Undergraduates or Beginning Graduates,
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This review is from: Advanced Quantum Mechanics (Hardcover)
The sub-title of this book is: The classical-quantum connection. This book is intended to be used by advanced undergraduate and early graduate students with a fairly sound background in mathematics and quantum mechanics. It does spend two chapters giving a review of the basic mathematics that will be used later, but it is at a level where most students would have liked to have covered this material in earlier courses. In these two chapters totaling about 65 pages the material from several math classes are quickly covered.
With this basic background covered, the book gives a review of Newtonian mechanics then the Schrodinger wave equation and periodic-orbit quantization and thence to more complex subjects. The book is aimed at the student who would like to be taken from basic quantum mechanics to periodic-orbit theory. Dr. Blümel is professor of physics at Wesleyan University. He is also the author of Foundations of Quantum Mechanics, From Photons to Quantum Computers.
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