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• W2604879984 abstract "In this paper we consider the three-dimensional Schr{o}dinger operator with a $delta$-interaction of strength $alpha > 0$ supported on an unbounded surface parametrized by the mapping $mathbb{R}^2ni xmapsto (x,beta f(x))$, where $beta in [0,infty)$ and $fcolon mathbb{R}^2rightarrowmathbb{R}$, $fnotequiv 0$, is a $C^2$-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrodinger operator coincides with $[-frac14alpha^2,+infty)$. We prove that for all sufficiently small $beta > 0$ its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit $beta rightarrow 0+$. In particular, this eigenvalue tends to $-frac14alpha^2$ exponentially fast as $betarightarrow 0+$." @default.
• W2604879984 created "2017-04-14" @default.
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• W2604879984 date "2018-01-01" @default.
• W2604879984 modified "2023-09-24" @default.
• W2604879984 title "Asymptotics of the bound state induced by <i>δ</i>-interaction supported on a weakly deformed plane" @default.
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• W2604879984 doi "https://doi.org/10.1063/1.5019931" @default.
• W2604879984 hasPublicationYear "2018" @default.
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