  We discuss exact solutions of the Schroedinger equation for the system of two
ultracold atoms confined in an axially symmetric harmonic potential. We
investigate different geometries of the trapping potential, in particular we
study the properties of eigenenergies and eigenfunctions for quasi-one- and
quasi-two-dimensional traps. We show that the quasi-one- and the
quasi-two-dimensional regimes for two atoms can be already realized in the
traps with moderately large (or small) ratios of the trapping frequencies in
the axial and the transverse directions. Finally, we apply our theory to
Feshbach resonances for trapped atoms. Introducing in our description an
energy-dependent scattering length we calculate analytically the eigenenergies
for two trapped atoms in the presence of a Feshbach resonance.
