Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 108, 12 pages      arXiv:0711.3347      https://doi.org/10.3842/SIGMA.2007.108
Contribution to the Proceedings of the 3-rd Microconference Analytic and Algebraic Methods III

Straight Quantum Waveguide with Robin Boundary Conditions

Martin Jílek
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Brehová 7, 11519 Prague, Czech Republic

Received August 10, 2007, in final form November 08, 2007; Published online November 21, 2007

Abstract
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.

Key words: quantum waveguides; bound states; Robin boundary conditions.

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