Bound states due to a strong delta interaction supported by a curved surface

0185713 - UJF-V 20033012 RIV GB eng J - Journal Article
Exner, Pavel - Kondej, S.
Bound states due to a strong delta interaction supported by a curved surface.
Journal of Physics. A - Mathematical and General Physics. Roč. 36, č. 2 (2003), s. 443-457. ISSN 0305-4470
R&D Projects: GA AV ČR IAA1048101
Institutional research plan: CEZ:AV0Z1048901
Keywords : quantum wave-guides * Schrodinger-operators * layers
Subject RIV: BE - Theoretical Physics
Impact factor: 1.357, year: 2003

We study the Schrodinger operator -Delta-alphadelta(x-Gamma) in L-2(R-3) with a delta interaction supported by an infinite non-planar surface Gamma with is smooth and admits a global normal parametrization with a uniformy elliptic metric. We show that if Gamma is asymptotically planar in a suitable sense and alpha > 0 is sufficiently large, this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a `two-dimensional` comparison operator determined by the geometry of the surface Gamma.
Permanent Link: http://hdl.handle.net/11104/0082096