Microlocal resolvent estimates for \(N\)-body Schrödinger operators. (English) Zbl 0810.35073

Wang, Xue Ping

J. Fac. Sci., Univ. Tokyo, Sect. I A 40, No. 2, 337-385 (1993).

Author’s abstract: “We use Mourre’s commutator method to establish a series of microlocal resolvent estimates with one or two sided microlocalizations for \(N\)-body Schrödinger operators with only mild regularity assumptions of potentials. Our results are optimal for \(N\)- body Schrödinger operators with the spectral structure of three-body operators (which in particular include three-body systems and \(N\)-body systems with repulsive potentials) and, in the general case, are almost optimal in high energy estimates. We also prove semiclassical microlocal resolvent estimates for a class of \(N\)-body operators with singular potentials”.

Reviewer: Chen Shuxing (Shanghai)

MSC:

35P25	Scattering theory for PDEs
35Q40	PDEs in connection with quantum mechanics
35Q55	NLS equations (nonlinear Schrödinger equations)
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis
35A27	Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs

Keywords:

microlocal resolvent estimates; semiclassical microlocal resolvent estimates