Skip to content
Register Sign in Wishlist
Spectral Asymptotics in the Semi-Classical Limit

Spectral Asymptotics in the Semi-Classical Limit

$79.99 (C)

Part of London Mathematical Society Lecture Note Series

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

$ 79.99 (C)
Paperback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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
    Read more

    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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: October 1999
    • format: Paperback
    • isbn: 9780521665445
    • length: 240 pages
    • dimensions: 228 x 154 x 15 mm
    • weight: 0.33kg
    • availability: 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.

  • Authors

    M. Dimassi, Université de Paris XIII

    J. Sjostrand, Ecole Polytechnique, Paris

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×