Vertically coupled non-uniform quantum rings with two separated electrons in threading magnetic field

We propose a simple method for calculating the energy spectrum of two separated electrons in vertically coupled narrow quantum rings with non-uniform cross-sections heights. We present numerical results for energies of some low-lying levels as a function of the magnetic flux for a particular case, in which one of two rings is uniform and other has a locally distorted height. The effect of the distortion on the Aharonov-Bohm oscillations is studied.