An Optimized Perfectly Matched Layer for the Schrödinger Equation (Communications in Computational Physics, 2011)
We derive a perfectly matched layer (PML) for the Schrödinger equation usinga modal ansatz. We derive approximate error formulas for the modeling error fromthe outer boundary of the PML and the error from the discretization in the layer andshow how to choose layer parameters so that these errors are matched and optimalperformance of the PML is obtained. Numerical computations in 1D and 2D demonstratethat the optimized PML works efficiently at a prescribed accuracy for the zeropotential case, with a layer of width less than a third of the de Broglie wavelengthcorresponding to the dominating frequency.