@PhDThesis{	  itlic:2013-005,
  author	= {Emil Kieri},
  title		= {Numerical Quantum Dynamics},
  school	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2013},
  number	= {2013-005},
  type		= {Licentiate thesis},
  month		= oct,
  day		= {15},
  note		= {Included papers available at
		  \url{http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179058},
		  \url{http://www.it.uu.se/research/publications/reports/2013-019/},
		  \url{http://www.it.uu.se/research/publications/reports/2013-007/}.}
		  ,
  abstract	= {We consider computational methods for simulating the
		  dynamics of molecular systems governed by the
		  time-dependent Schr{\"o}dinger equation. Solving the
		  Schr{\"o}dinger equation numerically poses a challenge due
		  to its often highly oscillatory solutions, and to the
		  exponential growth of work and memory with the number of
		  particles in the system.
		  
		  Two different classes of problems are studied: the dynamics
		  of the nuclei in a molecule and the dynamics of an electron
		  in orbit around a nucleus. For the first class of problems
		  we present new computational methods which exploit the
		  relation between quantum and classical dynamics in order to
		  make the computations more efficient. For the second class
		  of problems, the lack of regularity in the solution poses a
		  computational challenge. Using knowledge of the non-smooth
		  features of the solution we construct a new method with two
		  orders higher accuracy than what is achieved by direct
		  application of a difference stencil.}
}