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Spectral Asymptotics in the Semi-Classical Limit

Spectral Asymptotics in the Semi-Classical Limit


Part of London Mathematical Society Lecture Note Series

  • Date Published: September 1999
  • availability: Available
  • format: Paperback
  • isbn: 9780521665445

£ 26.99

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About the Authors
  • Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include 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. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.

    • Indispensable for researchers in this area
    • Authors are top names
    • Covers results from recent years
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    Reviews & endorsements

    '… recommended to everyone, be it student or researcher, who is interested in semiclassical analysis.' Zentralblatt MATH

    'This book is an excellent introduction to a modern rapidly developing subject which lies between mathematics and physics.' Yuri Safarov, Bulletin of the London Mathematical Society

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    Product details

    • Date Published: September 1999
    • format: Paperback
    • isbn: 9780521665445
    • length: 240 pages
    • dimensions: 228 x 154 x 15 mm
    • weight: 0.33kg
    • availability: Available
  • Table of Contents

    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
    Index of notation.

  • Authors

    M. Dimassi, Université de Paris XIII

    J. Sjostrand, Ecole Polytechnique, Paris

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