@TechReport{	  it:2009-017,
  author	= {Anna Nissen and Gunilla Kreiss},
  title		= {An Optimized Perfectly Matched Layer for the
		  {S}chr{\"o}dinger Equation},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2009},
  number	= {2009-017},
  month		= jun,
  abstract	= {A perfectly matched layer (PML) for the Schr{\"o}dinger
		  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.}
}