NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (2), P. 166–172
NOTE ON 2D SCHRÖDINGER OPERATORS WITH δ-INTERACTIONS ON ANGLES AND CROSSING LINES
V. Lotoreichik – Technische Universität Graz, Institut für Numerische Mathematik, Steyrergasse 30, 8010 Graz, Austria; lotoreichik@math.tugraz.at
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 δ-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 δ-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with δ-interactions between particles.
Keywords: Schrödinger operators, δ-interactions, spectral estimates.
PACS 03.65.-w