deletions | additions       diff --git a/Optimal control.tex b/Optimal control.tex  index 012f401..7c14d26 100644  --- a/Optimal control.tex  +++ b/Optimal control.tex 
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evolution of the system also depends on the value taken by those parameters:  \begin{equation}  {\rm i}\frac{{\rm d}}{{\rm d}t}\vert\psi(t)\rangle =  \hat{H}[u]\vert\psi(t)\rangle\,, \hat{H}[u,t]\vert\psi(t)\rangle\,,  \end{equation}  i.e. the solution of Schr{\"{o}}dinger's equation determines a map $u  \longrightarrow \psi[u]$ (QOCT can also be formulated in terms of von 
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handle that is used to control is a time-dependent electric field, such as the  ones that can be used to model a laser pulse. The parameters mentioned above  are used to define the shape of this electric field, i.e. they may be the  Fourier coefficients of the electric amplitude). Also, the usual formulation of QOCT assumes the linearity of quantum mechanics. However, the time-dependent Kohn-Sham equations are not linear, and this fact complicates both the theory and the numerics. We therefore extended the basic theory to handle the TDDFT equations, and implemented the resulting equations~\cite{Castro2012a}.