  Is it possible to trap a quantum particle in an open geometry? In this work
we deal with the boundary value problem of the stationary Schroedinger (or
Helmholtz) equation within a waveguide with straight segments and a rectangular
bending. The problem can be reduced to a one dimensional matrix Schroedinger
equation using two descriptions: oblique modes and conformal coordinates. We
use a corner-corrected WKB formalism to find the energies of the one
dimensional problem. It is shown that the presence of bound states is an effect
due to the boundary alone, with no classical counterpart for this geometry. The
conformal description proves to be simpler, as the coupling of transversal
modes is not essential in this case.
