Work

Bound States in Soft Quantum Layers

Year: 2024

Type: article

Abstract: We develop a general approach to study three-dimensional Schrödinger 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 Schrödinger 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 Schrödinger operator possesses an infinite number of discrete eigenvalues.

Source: Publications of the Research Institute for Mathematical Sciences

DOI: 10.4171/prims/60-4-4

Authors: David Krejčiřík, Jan Kříž

Institutions: Czech Technical University in Prague, University of Hradec Králové

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Grantová Agentura České Republiky

Award: New challenges for spectral theory: geometry, advanced materials and complex fields