Exciton formed by electron and hole separated in concentric quantum rings

We analyze a Wannier–Mott exciton in which the electron is constrained to move in a quantum ring and the hole moves in another concentric quantum rings. We expand the electron–hole interaction potential in terms of multipoles by assuming that both the electron and hole experience transverse harmonic confinements in the ρ and z directions, both being in their respective transverse groundstates. For the resulting φ-dependent Schrödinger equation we calculate the lowest exciton eigenenergies and eigenfunctions.