Long-range scattering of three-body quantum systems: Asymptotic completeness

摘要

This paper may be viewed as the first in a series of two papers on asymptotic completeness for (generalized) three-body quantum systems with long-range interaction. The model to be studied is given in terms of a finite family of subspaces (X_a|a ∈ F} of a finite dimensional Euclidean space X. By definition there exist a_(min), a_(max) ∈ F such that X_(a_(min)) = X and X_(a_(max)) = {0}, respectively, and for a and b different from a_(min) the "three-body" condition X_a ∩ X_b = {0} is imposed.