The numerical approximation of the solution of the time-dependent
Schrödinger equation arising in ultrafast laser dynamics is discussed.
The linear electronic Schrödinger equation is reduced to a
computationally tractable, lower dimensional system of nonlinear partial
differential equations by the
\emph{multi-configuration time-dependent Hartree-Fock method (MCTDHF)}. This method
uses an ansatz for the wave function on a nonlinear manifold,
taking into account the antisymmetry inherent in the model to reduce the dimension
of the solution space. We show that the ansatz used is consistent with the
original equation and the solution
can be represented exactly in principle using the solutions
of the nonlinear PDEs associated with MCTDHF. For the practical solution
of the MCTDHF equations, several numerical techniques are discussed, and it
is demonstrated that physically relevant problems can be solved satisfactorily.