Hiatus perturbation for a singular Schrodinger operator with an interaction supported by a curve in R-3

0309333 - ÚJF 2009 RIV US eng J - Journal Article
Exner, Pavel - Kondej, S.
Hiatus perturbation for a singular Schrodinger operator with an interaction supported by a curve in R-3.
[Porucha přerušením pro singulární Schrodingerův operátor s interakcí nesenou křivkou v R-3.]
Journal of Mathematical Physics. Roč. 49, č. 3 (2008), 032111/1-032111/3. ISSN 0022-2488. E-ISSN 1089-7658
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : delta-interaction * asymptotics
Subject RIV: BE - Theoretical Physics
Impact factor: 1.085, year: 2008

We consider Schrodinger operators in L-2(R-3) with a singular interaction supported by a finite curve Gamma. We present a proper definition of the operators and study their properties, in particular, we show that the discrete spectrum can be empty if Gamma is short enough. If it is not the case, we investigate properties of the eigenvalues in the situation when the curve has a hiatus of length 2 is an element of. We derive an asymptotic expansion with the leading term which a multiple of is an element of ln is an element of.

Vyšetřujeme singulární Schrodingerův operátor s interakcí nesenou křivkou v R-3 a odvozujeme asymptotické chování vlastních hodnot v případě, že křivka má přerušení délky 2/epsilon.
Permanent Link: http://hdl.handle.net/11104/0161490