J. Dittrich, J. Kriz
Curved planar quantum wires with Dirichlet and Neumann boundary conditions 
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ABSTRACT.  We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional curved strip. We impose the Dirichlet and Neumann boundary condition on opposite sides of the strip. The existence of the discrete eigenvalue below the essential spectrum threshold depends on the sign of the total bending angle for the asymptotically straight strips.