  In this paper we propose a modified Lie-type spectral splitting approximation
where the external potential is of quadratic type. It is proved that we can
approximate the solution to a one-dimensional nonlinear Schroedinger equation
by solving the linear problem and treating the nonlinear term separately, with
a rigorous estimate of the remainder term. Furthermore, we show by means of
numerical experiments that such a modified approximation is more efficient than
the standard one.
