  In this work, we analytically study the Schr\"odinger equation for the
(non-pure) dipolar ion potential V (r) = q/r + Dcos{\theta}/r 2 , in the case
of 2D systems using the separation of variables and the Mathieu equations for
the angular part. We give the expressions of eigenenergies and eigenfunctions
and study their dependence on the dipole moment D. Imposing the condition of
reality on the energies E n,m implies that the dipole moment must not exceed a
maximum value otherwise the corresponding bound state disappears. We also find
that the s states (m = 0) can no longer exist in the system as soon as the
dipole term is present.
