Does the Born-Oppenheimer approximation blur computational studies of laser-induced molecular quantum dynamics? An answer is difficult for various reasons. The underlying Schroedinger equations generate high-dimensional, highly oscillatory, multi-scale dynamics. Moreover, they have Hamiltonians with Coulomb singularities. In recent joint work with L. Adamowicz, S. Kvaal and T. Pederson we have computed laser-induced quantum dynamics for the hydrogen deuterium molecule in nine space dimensions, without invoking the Born-Oppenheimer approximation. Our talk will discuss the underlying basis construction that utilizes Gaussian functions of variable width and center and its numerical validation for one-dimensional model systems.