Spectral properties of soft quantum waveguides
Spectral Theory
2021-09-01 v3 Mathematical Physics
math.MP
Quantum Physics
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.
Cite
@article{arxiv.2006.15071,
title = {Spectral properties of soft quantum waveguides},
author = {Pavel Exner},
journal= {arXiv preprint arXiv:2006.15071},
year = {2021}
}
Comments
a few misprints and one minor inconsistency corrected