A perfectly matched layer (PML) for the Schrödinger equation using a modal ansatz is presented. We derive approximate error formulas for the modeling error from the outer boundary of the PML and for the error from the discretization and show how these can be matched in order to obtain optimal performance of the PML. Included numerical results show that the PML works efficiently at a prescribed accuracy for the zero potential case, with a layer of width less than two percent of the computational domain.
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