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Quasiclassical Methods

  • Book
  • © 1997

Overview

Editors:
  1. Jeffrey Rauch

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

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  2. Barry Simon

    1. Department of Mathematics, California Institute of Technology, Pasadena, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 95)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
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  4. Back Matter

    Pages 225-230
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Keywords

About this book

This IMA Volume in Mathematics and its Applications QUASICLASSICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun­ dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil­ tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec­ ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas­ sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. Two examples of this involve Weyl asymptotics and the large-Z limit of atomic Hamiltonians, both areas of current research.

Editors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Jeffrey Rauch

  • Department of Mathematics, California Institute of Technology, Pasadena, USA

    Barry Simon

Bibliographic Information

  • Book Title: Quasiclassical Methods

  • Editors: Jeffrey Rauch, Barry Simon

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4612-1940-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-98310-3Published: 03 October 1997

  • Softcover ISBN: 978-1-4612-7349-3Published: 02 October 2012

  • eBook ISBN: 978-1-4612-1940-8Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: IX, 230

  • Topics: Analysis

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