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

##### 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