  This is the third part of a paper about non-relativistic Schroedinger theory
on q-deformed quantum spaces like the braided line or the three-dimensional
q-deformed Euclidean space. Propagators for the free q-deformed particle are
derived and their basic properties are discussed. A time-dependent formulation
of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger
equation are given. Expressions for their iterative solutions are written down.
It is shown how to calculate S-matrices and transition probabilities.
Furthermore, attention is focused on the question what becomes of unitarity of
S-matrices in a q-deformed setting. The examinations are concluded by a
discussion of the interaction picture and its relation to scattering processes.
