Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV

Magnetic Schrödinger Operator 2
1. Auflage 2019
ISBN: 978-3-030-30547-5
Verlag: Springer Nature Switzerland

Buch, Englisch, 714 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1101 g

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, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.

Zielgruppe

Research

Autoren/Hrsg.

Ivrii, Victor

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Non-smooth theory and higher dimensions.- Irregular coefficients in dimensions 2, 3.- Full-rank case.- Non-full-rank case.- 4D-Schrödinger with degenerating magnetic field.- 4D-Schrödinger Operator with the strong magnetic field.- Eigenvalue asymptotics for Schrödinger and dirac operators with the strong magnetic field.- Eigenvalue asymptotics: 2D case.- Eigenvalue asymptotics: 3D case.

Über Autor(innen)

VICTOR IVRII is a professor of mathematics at the University of Toronto. His areas of specialization are analysis, microlocal analysis, spectral theory, partial differential equations and applications to mathematical physics. He proved the Weyl conjecture in 1979, and together with Israel M. Sigal he justified the Scott correction term for heavy atoms and molecules in 1992. He is a Fellow of the Royal Society of Canada (since 1998) and of American Mathematical Society (since 2012).