Schrodinger equation for non-pure dipole potential in 2D systems

In this work, we analytically study the Schrodinger equation for the (non-pure) dipolar ion potential V(r) = q/r + D cos theta/r(2), in the case of 2D systems (systems in two-dimensional Euclidean plane) using the separation of variables and the Mathieu equations for the angular part. We give the expressions of eigenenergies and eigen-functions and study their dependence on the dipole moment D. Imposing the condition of reality on the energies E-n,E-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. Published by AIP Publishing.