02-461 Pavel Exner and Sylwia Kondej

Bound states due to a strong $\delta$ interaction supported by a curved surface (63K, LaTeX) Nov 14, 02

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Abstract. 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]

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