@PhDThesis{	  itlic:2010-001,
  author	= {Anna Nissen},
  title		= {Absorbing Boundary Techniques for the Time-dependent
		  Schr{\"o}dinger Equation},
  school	= {Department of Information Technology, Uppsala University},
  year		= {2010},
  number	= {2010-001},
  type		= {Licentiate thesis},
  month		= feb,
  day		= {11},
  abstract	= {Chemical dissociation processes are important in quantum
		  dynamics. Such processes can be investigated theoretically
		  and numerically through the time-dependent Schr{\"o}dinger
		  equation, which gives a quantum mechanical description of
		  molecular dynamics.
		  
		  This thesis discusses the numerical simulation of chemical
		  reactions involving dissociation. In particular, an
		  accurate boundary treatment in terms of artificial,
		  absorbing boundaries of the computational domain is
		  considered. The approach taken here is based on the
		  perfectly matched layer technique in a finite difference
		  framework. The errors introduced due to the perfectly
		  matched layer can be divided into two categories, the
		  modeling error from the continuous model and numerical
		  reflections that arise for the discretized problem. We
		  analyze the different types of errors using plane wave
		  analysis, and parameters of the perfectly matched layer are
		  optimized so that the modeling error and the numerical
		  reflections are of the same order. The level of accuracy is
		  determined by estimating the order of the spatial error in
		  the interior domain. Numerical calculations show that this
		  procedure enables efficient calculations within a given
		  accuracy. We apply our perfectly matched layer to a
		  three-state system describing a one-dimensional IBr
		  molecule subjected to a laser field and to a
		  two-dimensional model problem treating dissociative
		  adsorbtion and associative desorption of a H2 molecule on a
		  solid surface. Comparisons made to standard absorbing
		  layers in chemical physics prove our approach to be
		  efficient, especially when high accuracy is of importance.}
}