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, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

Auteur

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).

Contenu

No magnetic field case.- The case of external magnetic field.- The case of self-generated magnetic field,- The case of combined magnetic field.- Articles on asymptotics.- 100 years of Weyl's law.