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. 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 co…
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- Full title :Bound states of the magnetic Schrödinger operator / Nicolas Raymond.
Summary
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. 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.
Read More ↓Edition Statements
- Publication Date:[2017].
Publication Statements
- Publisher(s):European Mathematical Society Publishing House
- Place of Publication:Zürich, Switzerland
- Language:eng
- Publication Date:[2017].
Notes
In European Mathematical Society.
The Physical Object
- Description:1 ressource en ligne (xiv, 380 pages).
Edition Identifiers
- ISBN:9783037196694, 3037196696
- DOI:10.4171/169
- oclc:ocn968525535
- LC Classification:QC174.17.S3
- Dewey Decimal:530.15/57222
Table of Contents
Part 1 Methods and examples -- Elements of Spectral Theory -- Examples -- First semiclassical examples -- From local models to global estimates -- Birkhoff normal form in dimension one -- Part 2 Main theorems -- Spectral reductions -- Mangnetic wells in dimension two -- Boundary magnetic wells in dimension three -- Waveguides -- On some connected non-linear problems -- Part 3 Spectral reductions -- Electric Born-Oppenheimer approximation -- Magnetic Born-Oppenheimer approximation -- Examples of magnetic WKB constructions -- Part 4 Magnetic wells in dimension two -- Vanishing magnetic fields in dimension two -- Non-vanishing magnetic fields -- Semiclassical non-linear magnetic eigenvalues -- Part 5 Boundary magnetic wells in dimension three -- Magnetic half-space -- Magnetic wedge -- Magnetic cone -- Part 6 Waveguides -- Magnetic effects in curved waveguides -- Spectrum of thin triangles and broken waveguides -- Non-linear dynamics in bidimensional waveguides.
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