# Trapped modes in finite quantum waveguides

@article{Delitsyn2011TrappedMI, title={Trapped modes in finite quantum waveguides}, author={A. L. Delitsyn and B.-T. Nguyen and Denis S. Grebenkov}, journal={The European Physical Journal B}, year={2011}, volume={85}, pages={1-12} }

The eigenstates of an electron in an infinite quantum waveguide (e.g., a bent strip or a twisted tube) are often trapped or localized in a bounded region that prohibits the electron transmission through the waveguide at the corresponding energies. We revisit this statement for resonators with long but finite branches that we call “finite waveguides”. Although the Laplace operator in bounded domains has no continuous spectrum and all eigenfunctions have finite L2 norm, the trapping of an…

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