Schroedinger operators with singular interactions: a model of tunneling resonances
Exner, Pavel ; Kondej, Sylwia
arXiv, 0312055 / Harvested from arXiv
Text on arXiv
We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if $d=2$, or surface waves in presence of a finite number of impurities if $d=3$. We analyze the discrete spectrum, and furthermore, we show that the resonance problem in this setting can be explicitly solved; by Birman-Schwinger method it is cast into a form similar to the Friedrichs model.
Publié le : 2003-12-22
Classification:  Mathematical Physics,  Condensed Matter - Mesoscale and Nanoscale Physics,  Mathematics - Spectral Theory,  Quantum Physics,  81V99 
@article{0312055,
     author = {Exner, Pavel and Kondej, Sylwia},
     title = {Schroedinger operators with singular interactions: a model of tunneling
  resonances},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312055}
}

Exner, Pavel; Kondej, Sylwia. Schroedinger operators with singular interactions: a model of tunneling
  resonances. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312055/