Microlocal Analysis, Sharp Spectral Asymptotics and Applications III: Magnetic Schrödinger Operator 1

Description

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3. Front Matter ....Pages I-XXI Front Matter ....Pages 1-1 Standard Theory in Dimensions 2 and 3 (Victor Ivrii)....Pages 2-181 \(2\mathsf {D}\)-Schrödinger Operator with the Strong Degenerating Magnetic Field (Victor Ivrii)....Pages 182-316 2D-Schrödinger Operator with the Strong Magnetic Field near Boundary (Victor Ivrii)....Pages 317-413 Front Matter ....Pages 414-414 Magnetic Schrödinger Operator: Short Loops, Pointwise Spectral Asymptotics and Asymptotics of Dirac Energy (Victor Ivrii)....Pages 415-563 Dirac Operator with the Strong Magnetic Field (Victor Ivrii)....Pages 564-646 Back Matter ....Pages 647-729