New splitting finite difference schemes for 2D and 3D linear Schrödinger problems are investigated. The stability and convergence analysis is done in the discrete L2 norm. It is proved that the 2D scheme is unconditionally stable and conservative in the case of zero boundary condition. The splitting scheme is generalized for 3D problems. It is proved that in this case the scheme is only ρ-stable and consequently discrete conservation laws are no longer valid. Results of numerical experiments are presented.
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