  We summarize some basics about mathematical tools of analysis for the
q-deformed Euclidean space. We use the new tools to examine q-deformed
eigenfunctions of the momentum or position operator within the framework of the
star product formalism. We show that these two systems of functions are
complete and orthonormal. With the q-deformed momentum or position
eigenfunctions, we calculate matrix elements of the momentum or position
operator. Considerations about expectation values and probability densities
conclude the studies.
