  We provide a simple sufficient condition in an abstract framework to deduce
the existence and completeness of wave operators (resp. modified wave
operators) on Sobolev spaces from the existence and completeness of the usual
wave operators (resp. modified wave operators). We then give some examples of
Schr\"odinger operators to which our abstract result applies. An application to
scattering theory for the nonlinear Schr\"odinger equation with a potential is
also given.
