Wave operators of Deift–Simon type for a class of Schrödinger evolutions. I

We are interested in questions of the scattering theory concerning the asymptotic behaviour of some Schrodinger evolutions. More precisely we present some results of the asymptotic completeness obtained by the method of Deift–Simoh wave operators recently developed in the theory of $N$-body systems. We consider here only the $2$-body case, treating a class of general time-dependent hamiltonians, e.g. $H(t)=H_0+V(t,x)$ with $H_0$ being a second order differential operator witli constant coefficients and $V(t,x)$ decaying suitably when $|x|\to\infty$.