Bound States in Two-dimensional Crossed or Bent Quantum Wires

Abstract

The method of conformal transformation is applied to solve the bound state problem for two-dimensional crossed wires with sharp and with smooth circular corners, for T-shaped and L-shaped wires and a number of other geometries. It is shown that in this method the wave equation with Dirichlet boundary condition on the boundaries of these wires can be transformed to a Schrödinger equation with a unique two-dimensional energy-dependent noneseparable potential. The results for various geometries indicate that sharp corners are essential in generating the bound states.