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We analyse a splitting integrator for the time discretization of theSchr\"odinger equation with nonlocal interaction cubic nonlinearity and whitenoise dispersion. We prove that this time integrator has order of convergenceone in the $p$-th mean sense, for any $p\geq1$ in some Sobolev spaces. We provethat the splitting schemes preserves the $L^2$-norm, which is a crucialproperty for the proof of the strong convergence result. Finally, numericalexperiments illustrate the performance of the proposed numerical scheme.

Strong rates of convergence of a splitting scheme for Schr\"{o}dinger  equations with nonlocal interaction cubic nonlinearity and white noise  dispersion