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arXiv · 2205.04919

Bound states in soft quantum layers

David Krejcirik·Jan Kriz
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Abstract

We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus in the Euclidean space. If the surface is asymptotically planar in a suitable sense, we give an estimate on the location of the essential spectrum of the Schroedinger operator. Moreover, if the surface coincides up to a compact subset with a surface of revolution with strictly positive total Gauss curvature, it is shown that the Schroedinger operator possesses an infinite number of discrete eigenvalues.

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David Krejcirik, Jan Kriz. 2022-05-10. Bound states in soft quantum layers. https://arxiv.org/abs/2205.04919

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