Abstract
The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schr\"odinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and lima\ifmmode \mbox{\c{c}}\else \c{c}\fi{}on-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov--Bohm oscillations.
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