Straight Quantum Waveguide with Robin Boundary Conditions - Jílek, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated eigenvalues and eigenfunctions are studied numerically by the mode-matching technique.