The quantum-mechanical
few-body problem has challenged physicists ever since the foundations of
quantum theory were laid in the 1920s. Collisions of atoms, molecules, and
their ions are particularly interesting realizations of this problem, because
the interaction potentials are well known and the question of how to deal with
the few-body character of the collision system under study is the only
fundamental difficulty for theory. Given the abundance of available experimental
data and the importance of understanding them not just for fundamental but also
for applied reasons, there is considerable motivation to address this
difficulty.

The objective of this talk is to illustrate these statements using examples
drawn from recent research in the field. In particular, a time-dependent
quantum-mechanical approach based on the concepts of density functional theory
will be outlined and applied to three-electron collision systems involving
helium and lithium atoms. It will be demonstrated that depending on the process
under study the few-body problem presents itself as a more or less intricate
one. I will discuss situations which reflect single-active-electron dynamics,
independent-electron dynamics and more complicated, i.e., correlated, electron
dynamics.

PLEASE NOTE NON STANDARD LOCATION