  We consider the defocusing nonlinear Schr{\"o}dinger equation in several
space dimensions, in the presence of an external potential depending on only
one space vari-able. This potential is bounded from below, and may grow
arbitrarily fast at infinity. We prove existence and uniqueness in the
associated Cauchy problem, in a suitable functional framework, as well as the
existence of wave operators when the power of the nonlinearity is sufficiently
large. Asymptotic completeness then stems from at least two approaches, which
are briefly recalled.
