Quasiclassical Methods

Herausgegeben:Rauch, Jeffrey; Simon, Barry

• Broschiertes Buch

Produktbeschreibung

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 correspondingclassical 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.

Produktdetails

• The IMA Volumes in Mathematics and its Applications 95
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4612-7349-3
• Softcover reprint of the original 1st ed. 1997
• Seitenzahl: 244
• Erscheinungstermin: 2. Oktober 2012
• Englisch
• Abmessung: 235mm x 155mm x 14mm
• Gewicht: 379g
• ISBN-13: 9781461273493
• ISBN-10: 1461273498
• Artikelnr.: 36937514

Autorenporträt

The chapters in this volume explore the various aspects of quasiclassical methods such as approximate theories for large Coulomb systems, Schroedinger operator with magnetic wells, ground state energy of heavy molecules in strong magnetic field, and methods with emphasis on coherent states. Included are also mathematical theories dealing with h-pseudodifferential operators, asymptotic distribution of eigenvalues in gaps, a proof of the strong Scott conjecture, Lieb- Thirring inequalities for the Pauli operator, and local trace formulae.

Inhaltsangabe

Tutorial Overviews.- h-pseudodifferential operators and applications: An introduction.- Semi-classical methods with emphasis on coherent states.- Workshop Research Papers.- Approximative theories for large Coulomb systems.- Semiclassical analysis for the Schrödinger operator with magnetic wells (after R. Montgomery, B. Helffer-A. Mohamed).- On the asymptotic distribution of eigenvalues in gaps.- Asymptotics of the ground state energy of heavy molecules in the strong magnetic field.- Local trace formulæ.- A proof of the strong Scott conjecture.- Lieb-Thirring inequalities for the Pauli operator in three dimensions.- Exact anharmonic quantization condition (in one dimension).