TL;DR
This course provides a comprehensive introduction to Weyl quantization and semiclassical analysis, covering classical and quantum mechanics, mathematical preliminaries, and applications to Born-Oppenheimer systems, aimed at graduate students in physics and mathematics.
Contribution
It offers an integrated educational resource on Weyl quantization and semiclassics, including mathematical foundations and practical applications, which is novel in its pedagogical approach.
Findings
Detailed overview of classical and quantum mechanics on R^d
Mathematical preliminaries on Hilbert spaces and operator theory
Application of Weyl calculus to Born-Oppenheimer systems
Abstract
This course is aimed at graduate students in physics in mathematics and designed to give a comprehensive introduction to Weyl quantization and semiclassics via Egorov's theorem. Chapter 2 gives a quick overview of classical and quantum mechanics on R^d. Some mathematical preliminaries concerning Hilbert space theory, operator theory and tempered distributions are detailed in Chapters 3-5. Weyl quantization and semiclassics are the content of Chapters 6 and 7. Finally, an application of Weyl calculus to Born-Oppenheimer systems is discussed in Chapter 8.
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Taxonomy
TopicsOptical and Acousto-Optic Technologies · Photonic and Optical Devices