In this work, we analytically study the Schrödinger equation for the (non-pure) dipolar ion potential V(r) = q/r + Dcosθ/r2, 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 eigenfunctions and study their dependence on the dipole moment D. Imposing the condition of reality on the energies En,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.
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2016
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