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  3. Spectral Asymptotics in the Semi-Classical Limit
  • Cited by 424
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2010
      September 1999
      ISBN:
      9780511662195
      9780521665445
      DOI:
      https://doi.org/10.1017/CBO9780511662195
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.33kg, 240 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      London Mathematical Society Lecture Note Series (268)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    London Mathematical Society Lecture Note Series (268)
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    Book description

    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.

    Reviews

    ‘… recommended to everyone, be it student or researcher, who is interested in semiclassical analysis.’

    Source: Zentralblatt MATH

    ‘This book is an excellent introduction to a modern rapidly developing subject which lies between mathematics and physics.’

    Yuri Safarov Source: Bulletin of the London Mathematical Society

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