Spectral theory for Schrödinger operators with δ-interactions supported on curves in ℝ³

2018/11/07 by Behrndt, Jussi, Frank, Rupert L., Kühn, Christian +2
#Mathematik #Schrödinger operators

paper · doi:10.15480/882.1775

Abstract

The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrödinger operators with δ-interactions supported on closed curves in R3. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten–von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.

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