Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV : Magnetic Schrödinger Operator 2. 1st ed. 2019

種類:

電子ブック

責任表示:

by Victor Ivrii

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Ivrii, Victor.
• SpringerLink (Online service)

ISBN:

9783030305451 [3030305457]    

注記:

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.
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.

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