Scattering matrix, phase shift, spectral shift and trace formula for one-dimensional Schrödinger-type operators
- Neidhardt, Hagen
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 47A20 47B44 47A40
- dissipative Schroedinger-type operators, Sturm-Liouville operators, self-adjoint dilation, characteristic function, Lax-Phillips scattering theory, scattering matrix, phase shift, spectral shift, trace formula, Birman-Krein formula
The paper is devoted to Schroedinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed, in particular, trace formula and Birman-Krein formula are verified directly. The results are used for dissipative Schroedinger-Poisson systems.
- Integral Equations Operator Theory, 58 (2007) pp. 407--431.