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

Springer, 2019. — 750 p. — ISBN: 978-3-030-30536-9.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.Standard Theory in Dimensions 2 and 3
2D-Schrödinger Operator with the Strong Degenerating Magnetic Field
2D-Schrödinger Operator with the Strong Magnetic Field near Boundary
Magnetic Schrödinger Operator: Short Loops, Pointwise Spectral Asymptotics and Asymptotics of Dirac Energy
Dirac Operator with the Strong Magnetic Field