Pavel Exner, Sylwia Kondej
Published 2002-07-19, updated 2002-11-14Version 2
We study the Schr\"odinger operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\R^3)$ with a $\delta$ interaction supported by an infinite non-planar surface $\Gamma$ which is smooth, admits a global normal parameterization with a uniformly 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 $\Gamma$. [A revised version, to appear in J. Phys. A]
Comments: LaTeX 2e, 21 pages
Journal: J. Phys. A36 (2003), 443-457
The Schrödinger particle on the half-line with an attractive $δ$-interaction: bound states and resonances
On the Number of Bound States of Finitely Many Point Interactions on Riemannian Manifolds
The self-energy of Friedrichs-Lee models and its application to bound states and resonances
