  The Gross-Pitaevskii equation with white noise in time perturbations of the
harmonic potential is considered. In this article we define a Crank-Nicolson
scheme based on a spectral discretization and we show the convergence of this
scheme in the case of cubic non-linearity and when the exact solution is
uniquely defined and global in time. We prove that the strong order of
convergence in probability is at least one.
