Related papers: Bound states in soft quantum layers

Bound states in soft quantum layers

URL: http://arxiv.org/abs/2205.04919v2
Date: Thu, 13 Apr 2023 13:43:04 GMT
Title: Bound states in soft quantum layers
Authors: David Krejcirik and Jan Kriz
Abstract summary: We study 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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