Jílek, Martin

Straight quantum waveguide with Robin boundary conditions

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 108, 12 p., electronic only (2007)


Summary: 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.

Mathematics Subject Classification

47F05, 47B25, 81Q05


quantum waveguides, bound states, Robin boundary conditions