Remarks on the spectral theory for the multiparticle-type Schrödinger operator

Abstract

Mourre's method is used to prove the limiting absorption principle for the multiparticle Schrödinger operator under the same assumptions on the pair potentials as in the two-particle problem. It is shown that at high energies this principle is valid under wider conditions than on the whole spectral axis. The scattering theory for a Schrödinger operator whose potential decays at infinity in an essentially anisotropic manner is constructed in analogy with the three-particle problem.