Spectral Asymptotics in the Semi-Classical Limit
Spectral Asymptotics in the Semi-Classical Limit
CAD$91.95
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. In recent years mathematical theory has undergone significant growth, mainly due to microlocal analysis techniques. This volume develops the basic methods of the theory, including the WKB-method, stationary phase and h-pseudodifferential operators. The authors employ the systematic use of a Cauchy formula that simplifies the functional calculus of pseudodifferential operators. The applications described include recent results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. The text assumes no previous specialized knowledge in quantum mechanics or microlocal analysis, and only general knowledge of spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry.
- Indispensable for researchers in this area
- Authors are top names
- Covers results from recent years
Reviews & endorsements
"Researchers and graduate students in mathematical analysis are the intended readership, but anyone with an interest in the current state of the mathematics of quantum mechanics will get a lot out of this book." Proceedings of the Edinburgh Mathematical Society
"The authors have managed to write a very useful, clear, and readable book of quite moderate size, applying modern sophisticated methods in order to attack successfully some important, interesting, and difficult problems of contemporary mathematical physics." Mathematical Reviews
Product details
October 1999Paperback
9780521665445
240 pages
228 × 154 × 15 mm
0.33kg
Available
Table of Contents
- Introduction
- 1. Local symplectic geometry
- 2. The WKB-method
- 3. The WKB-method for a potential minimum
- 4. Self-adjoint operators
- 5. The method of stationary phase
- 6. Tunnel effect and interaction matrix
- 7. h-pseudodifferential operators
- 8. Functional calculus for pseudodifferential operators
- 9. Trace class operators and applications of the functional calculus
- 10. More precise spectral asymptotics for non-critical Hamiltonians
- 11. Improvement when the periodic trajectories form a set of measure 0
- 12. A more general study of the trace
- 13. Spectral theory for perturbed periodic problems
- 14. Normal forms for some scalar pseudodifferential operators
- 15. Spectrum of operators with periodic bicharacteristics
- References
- Index
- Index of notation.
