Bound States Of The Magnetic Schrödinger Operator

Nicolas Raymond Tr a c ts i n M a t h e m a t i c s 2 7 Nicolas Raymond Bound States of the Magnetic Schrödinger Operator Since the presentation involves many notions of spectral theory and semiclassical analysis, it begins with a concise account of concepts and methods used in the book and is illustrated by many elementary examples. Assuming various points of view (power series expansions, Feshbach– Grushin reductions, WKB constructions, coherent states decompositions, normal forms) a theory of Magnetic Harmonic Approximation is then established which allows, in particular, accurate descriptions of the magnetic eigenvalues and eigenfunctions. Some parts of this theory, such as those related to spectral reductions or waveguides, are still accessible to advanced students while others (e.g., the discussion of the Birkhoff normal form and its spectral consequences, or the results related to boundary magnetic wells in dimension three) are intended for seasoned researchers. ISBN 978-3-03719-169-9 www.ems-ph.org Raymond | Tracts in Mathematics 27 | Fonts Nuri /Helvetica Neue | Farben Pantone 116 / Pantone 287 | RB 35 mm Bound States of the Magnetic Schrödinger Operator This book is a synthesis of recent advances in the spectral theory of the magnetic Schrödinger operator. It can be considered a catalog of concrete examples of magnetic spectral asymptotics. Tr a c ts i n M a t h e m a t i c s 2 7 Nicolas Raymond Bound States of the Magnetic Schrödinger Operator EMS Tracts in Mathematics 27 EMS Tracts in Mathematics Editorial Board: Michael Farber (Queen Mary University of London, Great Britain) Carlos E. Kenig (The University of Chicago, USA) Michael Röckner (Universität Bielefeld, Germany, and Purdue University, USA) Vladimir Turaev (Indiana University, Bloomington, USA) Alexander Varchenko (The University of North Carolina at Chapel Hill, USA) This series includes advanced texts and monographs covering all fields in pure and applied mathematics. Tracts will give a reliable introduction and reference to special fields of current research. The books in the series will in most cases be authored monographs, although edited volumes may be published if appropriate. They are addressed to graduate students seeking access to research topics as well as to the experts in the field working at the frontier of research. For a complete listing see our homepage at www.ems-ph.org. 10 Vladimir Turaev, Homotopy Quantum Field Theory 11 Hans Triebel, Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration 12 Erich Novak and Henryk