Hunziker, W., Sigal, I.M.
Time-Dependent Scattering Theory of N-Body Quantum Systems
(511K, PS-Adobe-2.0)
ABSTRACT. We give a full and selfcontained account
of the basic results in $N$--body scattering theory which emerged over
the last ten years: The existence and completeness of scattering states
for potentials decreasing like $r^{-\mu}$, $\mu>\sqrt{3}-1$ . Our approach
is a synthesis of earlier work and of new ideas.
Global conditions on the potentials are imposed only to
define the dynamics. Asymptotic completeness is derived from the fact that
the mean square diameter of the system diverges like\ \ $t^2$\ \
as\ \ $t\to \pm\infty$\ \ for any orbit $\psi_t$
which is separated in energy from thresholds and
eigenvalues (a generalized version of Mourre's theorem involving
only the tails of the potentials at large distances). We introduce
new propagation observables which considerably simplify the phase--space
analysis. As a topic of general interest we describe a method of
commutator expansions.