Geodesic
Note on 2D Schr\"odinger operators with $\delta$-interactions on angles and crossing lines
Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 2, pp. 166-172

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In this note we sharpen the lower bound previously obtained by Lobanov et al [LLP10] for the spectrum of the 2D Schrödinger operator with a $\delta$-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D Schrödinger operator with a $\delta$-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with $\delta$-interactions between particles.
Keywords: Schrödinger operators, $\delta$-interactions, spectral estimates. 
@article{NANO_2013_4_2_a0,
     author = {V. Yu. Lotoreichik},
     title = {Note on {2D} {Schr\"odinger} operators with $\delta$-interactions on angles and crossing lines},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {166--172},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2013_4_2_a0/}
}
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V. Yu. Lotoreichik. Note on 2D Schr\"odinger operators with $\delta$-interactions on angles and crossing lines. Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 2, pp. 166-172. http://geodesic.mathdoc.fr/item/NANO_2013_4_2_a0/