In this paper it is demonstrated how rigorous numerics may be applied to the
one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to
determining bound--state solutions and establishing certain spectral properties
of the linearization. Since the results are rigorous, they can be used to
complete a recent analytical proof [6] of the local exact controllability of
NLS.Comment: 30 pages, 2 figure
