N-body long-range scattering matrix

Abstract

We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions proving existence of radial limits of the functions and show that these scattering matrices are equivalent to the ones defined by wave operator approach in long-range N-body problems including the problems of Coulomb interaction potentials. Equivalence of stationary and time-dependent definitions of the generalized Fourier transforms is also shown.