Related papers: Spectral properties of soft quantum waveguides

Spectral properties of soft quantum waveguides

URL: http://arxiv.org/abs/2006.15071v3
Date: Tue, 31 Aug 2021 12:35:24 GMT
Title: Spectral properties of soft quantum waveguides
Authors: Pavel Exner
Abstract summary: We consider a soft quantum waveguide described by a two-dimensional Schr"odinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve. We show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough.
Score: 0.0
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We consider a soft quantum waveguide described by a two-dimensional Schr\"odinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned.

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