@TechReport{	  it:2009-021,
  author	= {Katharina Kormann and Sverker Holmgren and Hans O.
		  Karlsson},
  title		= {Global Error Control of the Time-Propagation for the
		  {S}chr{\"o}dinger Equation with a Time-Dependent
		  {H}amiltonian},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2009},
  number	= {2009-021},
  month		= sep,
  abstract	= {We use a posteriori error estimation theory to derive a
		  relation between local and global error in the propagation
		  for the time-dependent Schr\"odinger equation. Based on
		  this result, we design a class of $h,p$-adaptive
		  Magnus--Lanczos propagators capable of controlling the
		  global error of the time-stepping scheme by only solving
		  the equation once. We provide results for models of several
		  different small molecules including bounded and
		  dissociative states, illustrating the efficiency and wide
		  applicability of the new methods. }
}