We discuss the multi-configuration
time-dependent Hartree (MCTDH) method for the approximation
of the time-dependent Schrödinger equation in quantum molecular dynamics.
This method approximates the high-dimensional
wave function 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
time-dependent variational principle,
consist of a coupled system of ordinary and low-dimensional
nonlinear partial differential equations.
We show that the MCTDH equations
are well-posed as long as a full-rank condition remains satisfied.
The solution is shown to be regular enough to ensure
quasi-optimality of the approximation over short time intervals
and to admit an efficient numerical treatment if the potential
is sufficiently smooth.