02633nam 22004695a 450 991015539710332120161205234500.03-03719-669-610.4171/169(CKB)3710000000974732(CH-001817-3)212-161205(PPN)197530788(EXLCZ)99371000000097473220161205j20170101 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierBound States of the Magnetic Schrödinger Operator[electronic resource] /Nicolas RaymondZuerich, Switzerland European Mathematical Society Publishing House20171 online resource (394 pages)EMS Tracts in Mathematics (ETM)273-03719-169-4 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.Differential equationsbicsscMathematical logicbicsscPartial differential equationsmscCalculus of variations and optimal control; optimizationmscQuantum theorymscDifferential equationsMathematical logicPartial differential equationsCalculus of variations and optimal control; optimizationQuantum theory35-xx49-xx81-xxmscRaymond Nicolas1071334ch0018173BOOK9910155397103321Bound States of the Magnetic Schrödinger Operator2566821UNINA