Schrodinger Equation for Non-Pure Dipole Potential in 2D Systems

In this work, we analytically study the Schr"odinger equation for the (non-pure) dipolar ion potential V ® = 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.