deletions | additions       diff --git a/Schroedinger equation.tex b/Schroedinger equation.tex  index bfc3cd7..f23a412 100644  --- a/Schroedinger equation.tex  +++ b/Schroedinger equation.tex 
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\label{eq:SENd}  \hat{H}\Psi_j(x_1...x_N)=E_j\Psi_j(x_1...x_N)  \end{equation}  which provides a spatial wave function for a single particle in $N$ dimensions. This equivalence is not restricted to one-dimensional problems. One can generally map a problem of $N$ electrons in $d$ dimensions onto the problem of a single particle in $Nd$ dimensions, or indeed a problem with multiple types of particles (e.g. electrons and protons) in $d$ dimensions, in the same way. What we exploit in octopus is the basic machinery for solving the Sch\"odinger equation iteratively, the spatial/grid bookkeeping, and the intrinsic parallelization. In order to keep our notation relatively simple, we will continue to discuss the case of an originally one-dimensional problem with $N$ electrons. Grid-based resolutions of the full Schr\"odinger equation are not new, and have been performed for many problems with either few electrons (in particulare.g.  H$_2$ (or D$_2$) and H$_2^+$\cite{Ranitovic21012014} and H$_2^+$ e.g. in \cite{Ranitovic21012014} or  \cite{lein2002}) or model interactions\cite{luo2013,ramsden2012}. interactions\cite{luo2013}, including time dependent cases\cite{ramsden2012}.  %% @article{Ranitovic21012014, author = {Ranitovic, Predrag and Hogle, Craig W. and Rivière, Paula and Palacios, Alicia and Tong, Xiao-Ming and Toshima, Nobuyuki and González-Castrillo, Alberto and Martin, Leigh and Martín, Fernando and Murnane, Margaret M. and Kapteyn, Henry}, title = {Attosecond vacuum UV coherent control of molecular dynamics}, volume = {111}, number = {3}, pages = {912-917}, year = {2014}, optdoi = {10.1073/pnas.1321999111}, journal = {Proceedings of the National Academy of Sciences} }  %% @article{lein2002, title = {Strong-field ionization dynamics of a model ${\mathrm{H}}_{2}$ molecule}, author = {Lein, Manfred and Kreibich, Thomas and Gross, E. K. U. and Engel, Volker}, journal = {Phys. Rev. A}, volume = {65}, issue = {3}, pages = {033403}, year = {2002}, optdoi = {10.1103/PhysRevA.65.033403}}  %% @article{luo2013, title = {Absence of dynamical steps in the exact correlation potential in the linear response regime}, author = {Luo, Kai and Elliott, Peter and Maitra, Neepa T.}, journal = {Phys. Rev. A}, volume = {88}, issue = {4}, pages = {042508}, year = {2013}, optdoi = {10.1103/PhysRevA.88.042508} }