  The aim of Part II of this paper is to try to describe wave functions on
q-deformed versions of position and momentum space. This task is done within
the framework developed in Part I of the paper. In order to make Part II
self-contained the most important results of Part I are reviewed. Then it is
shown that q-deformed exponentials and q-deformed delta functions play the role
of momentum and position eigenfunctions, respectively. Their completeness and
orthonormality relations are derived. For both bases of eigenfunctions matrix
elements of position and momentum operators are calculated. A q-deformed
version of the spectral decomposition of multiplication operators is discussed
and q-analogs of Heaviside functions are proposed. Interpreting the results
from the point of view provided by the concept of quasipoints gives the
formalism a physical meaning. The definition of expectation values and the
calculation of probability densities are explained in detail. Finally, it is
outlined how the considerations so far carry over to antisymmetrized spaces.
