Synopses & Reviews
Synopsis
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for wide classes of partial differential operators using technique of semiclassical microlocal analysis, in particular, propagation of singularities, and to use the variational estimates in "small" domains to consider domains with singularities of different kinds. Then the general theory (results and developed methods) is applied to the Magnetic Schr dinger operator, miscellaneous problems and multiparticle quantum theory.
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.
Synopsis
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