Bound states and threshold resonances in quantum wires with circular bends.

We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, T and R and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions. †Present address: Department of Physics, 366 LeConte Hall, University of California at Berkeley, Berkeley, CA 94720 ∗This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative agreement #DF-FC02-94ER40818 and #DE-FG02-92ER40702 and in part by funds provided by the National Science Foundation under grant # PHY 92-18167