Quantum anticentrifugal potential in a bent waveguide

Abstract

We show the existence of an anticentrifugal force for a quantum particle in a bent waveguide. This counterintuitive force due to dimensionality was shown to exist in a flat $R^2$ space but there it needs an additional $\delta$-like potential at the origin in order to brake the translational invariance and to exhibit localized states. In the case of the bent waveguide there is no need of any additional potential since here the boundary conditions break the symmetry. The effect may be observed in interference experiments which are sensitive to the additional phase of the wavefunction gained in the bent regions and can find application in distinguishing between straight and bent geometries.