Bound States of the Magnetic Schrödinger Operator [electronic resource] / Nicolas Raymond
Material type: TextSeries: EMS Tracts in Mathematics (ETM) ; 27Publisher: Zuerich, Switzerland : European Mathematical Society Publishing House, 2017Description: 1 online resource (394 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783037196694Subject(s): Differential equations | Mathematical logic | Partial differential equations | Calculus of variations and optimal control; optimization | Quantum theoryOther classification: 35-xx | 49-xx | 81-xx Online resources: Click here to access online | cover image 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.Current library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK13880 |
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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.
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