Doctor of Philosophy / Department of Physics / Uwe Thumm / The time-dependent Schrödinger equation is integrated on a numerical lattice for up to three-dimensional problems. The wave packet propagation technique has been applied to ion – atom collisions in a strong laser field, the vibrational nuclear motion in small homonuclear diatomic molecular ions, and for the scattering of an ion in front of a metallic surface. For laser-assisted proton – hydrogen collisions it is shown, that strong circularly polarized radiation significantly alters the capture and ionization probabilities and results in a dichroism with respect to the helicity. In a pump – control – probe scheme, “stroboscopic” exposure of a nuclear wave packet of the deuterium molecular ion by a single or a series of short and intense laser control pulses may be used to produce an almost stationary distribution of a single vibrational level, where the nodal structure can be tested using the Coulomb explosion imaging technique. Using a pump – probe setup with variable probe delays it is proposed to use Fourier analysis of the time dependence of the Coulomb explosion kinetic energy release spectrum to reveal insight into the initial vibrational state distribution for small diatomic molecules. A last application demonstrates, that resonant charge transfer for scattering of a negative hydrogen anion on a metal surface depends crucially on the position of surface and image states relative to the conduction and valence band, thereby implying different reaction mechanisms for different surface cuts of a metal.