@TechReport{	  it:2009-022,
  author	= {Katharina Kormann and Sverker Holmgren and Hans O.
		  Karlsson},
  title		= {A {F}ourier-Coefficient Based Solution of an Optimal
		  Control Problem in Quantum Chemistry},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2009},
  number	= {2009-022},
  month		= sep,
  abstract	= {We consider an optimal control problem for the
		  time-dependent Schr{\"o}dinger equation modeling molecular
		  dynamics. Given a molecule in its ground state, the
		  interaction with a tuned laser pulse can result in an
		  excitation to a state of interest. By these means, one can
		  optimize the yield of chemical reactions. The problem of
		  designing an optimal laser pulse can be posed as an optimal
		  control problem. We reformulate the optimization problem by
		  Fourier-transforming the electric field of the laser and
		  narrow the frequency band. In this way, we reduce the
		  dimensionality of the control variable. This allows for
		  storing an approximate Hessian and, thereby, we can solve
		  the optimization problem with a quasi-Newton method. Such
		  an implementation provides superlinear convergence. We show
		  computational results for a Raman-transition example and
		  give numerical evidence that our algorithm can outperform
		  the standard Krotov-like method which does not employ
		  approximative second derivatives. \end{abstract} }
}