Spectral and transport characteristics of an arbitrarily bent planar quantum electron guide

The spectral and stationary scattering problems of noninteracting electrons in a two-dimensional (2D) quantum electron guide of constant width, an arbitrary bending angle, and an extremely sharp bend, are shown to be reduced to the same problems in a straight 2D quantum electron guide with two additional bend-imitating matching conditions on jumps of the probability amplitude and its longitudinal derivative. In the framework of this approach the energy of lowest bound state and its dependence on the bending angle have been calculated. The dependences of transition and reflection coefficients on the electron energy and on the bending angle have been obtained. The bend-imitating model for the steady-state quantum-mechanical treatment of multiple-bend quantum wire has also been explicitly formulated. The II-like and Z-like shaped wires are shown to possess a split lowest bound state. The dependences of the splitting on the distance between the bends and the bending angles are calculated.