| Spectral Asymptotics in the Semi-Classical Limit Contributor(s): Dimassi, M. (Author), Dimassi, Mouez (Author), Sjostrand, J. (Author) |
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ISBN: 0521665442 ISBN-13: 9780521665445 Publisher: Cambridge University Press OUR PRICE: $75.99 Product Type: Paperback - Other Formats Published: October 1999 Annotation: 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 Schrodinger 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. |
| Additional Information |
| BISAC Categories: - Science | Physics - Mathematical & Computational - Medical - Mathematics | Probability & Statistics - General |
| Dewey: 530.155 |
| LCCN: 00267617 |
| Series: London Mathematical Society Lecture Notes |
| Physical Information: 0.52" H x 6.06" W x 9.03" (0.71 lbs) 240 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 Schr dinger 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. |