  We prove decay and scattering of solutions of the Nonlinear Schr\"oding-er
equation (NLS) in ${\mathbf R}$ with pure power nonlinearity with exponent
$3<p<5$ when the initial datum is small in $\Sigma$ (bounded energy and
variance), in the presence of a linear inhomogeneity represented by a linear
potential which is a real valued Schwarz function. We assume absence of
discrete modes. The proof is analogous to the one for the translation invariant
equation. In particular we find appropriate operators commuting with the
linearization.
