WIAS Preprint No. 1045, (2005)

Scattering matrix, phase shift, spectral shift and trace formula for one-dimensional Schrödinger-type operators



Authors

  • Neidhardt, Hagen
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 47A20 47B44 47A40

Keywords

  • 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

Abstract

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.

Appeared in

  • Integral Equations Operator Theory, 58 (2007) pp. 407--431.

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