Scattering matrices and Weyl functions

Abstract

For a scattering system $\{A_{\Theta },A_0\}$ consisting of selfadjoint extensions $A_{\Theta }$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\{S_\gT(\gl)\}$ and a spectral shift function ${\xi }_{\Theta }$ are calculated in terms of the Weyl function associated with the boundary triplet for $A^{\ast }$ and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar and matrix potentials, to Dirac operators and to Schrödinger operators with point interactions.

39 pages

Cited by in corpus (17)

• On an inverse problem for tree-like networks of elastic strings
• One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
• Spectral estimates for resolvent differences of self-adjoint elliptic operators
• High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line
• Scattering Theory for the matrix Schrödinger operator on the half line with general boundary conditions
• On Eisenbud's and Wigner's R-matrix: A general approach
• Approximation of one-dimensional relativistic point interactions by regular potentials revised
• Dynamics of an electron confined to a "hybrid plane" and interacting with a magnetic field
• Edge switching transformations of quantum graphs
• Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions
• Boundary triplets, tensor products and point contacts to reservoirs
• Non-compact quantum graphs with summable matrix potentials
• A quantum hybrid with a thin antenna at the vertex of a wedge
• Wave operators, similarity and dynamics for a class of Schroedinger operators with generic non-mixed interface conditions in 1D
• Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions
• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• A quantum evolution problem in the regime of quantum wells in a semiclassical island with artificial interface conditions