02435nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084002900202100003100231245009700262260008200359300003400441336002600475337002600501338003600527347002400563490004000587506006600627520106100693650003501754650003101789650004001820650006601860650002401926856003201950856006701982212-161205CH-001817-320161205234500.0a fot ||| 0|cr nn mmmmamaa161205e20170101sz fot ||| 0|eng d a978303719669470a10.4171/1692doi ach0018173 7aPBKJ2bicssc 7aPBCD2bicssc a35-xxa49-xxa81-xx2msc1 aRaymond, Nicolas,eauthor.10aBound States of the Magnetic Schrödinger Operatorh[electronic resource] /cNicolas Raymond3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (394 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v271 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis 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.07aDifferential equations2bicssc07aMathematical logic2bicssc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/169423cover imageuhttps://www.ems-ph.org/img/books/raymond_mini.jpg