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O. Koch, C. Lubich:
"Analysis and time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics";
in: "ASC Report 04/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

We discuss existence, regularity and numerical approximation of
the solution to the multi-configuration time-dependent Hartree-Fock (MCTDHF)
equations in quantum dynamics. This method approximates the highdimensional
solution to the time-dependent electronic Schr¨odinger equation by
a linear combination of products of functions depending only on a single degree
of freedom. The equations of motion, obtained via the Dirac-Frenkel timedependent
variational principle, consist of a coupled system of low-dimensional
nonlinear partial differential equations and ordinary differential equations. We
show that the MCTDHF equations have a global solution in the Sobolev space
H2 if the initial data has the same regularity. Moreover, we investigate the
convergence of a time integrator based on splitting of the vector field. First
order convergence in the H1 norm and second order convergence in L2 are
established

http://www.asc.tuwien.ac.at/preprint/2008/asc04x2008.pdf