WIAS Preprint No. 1076, (2005)

Block operator matrices, optical potentials, trace class perturbations and scattering



Authors

  • Behrndt, Jussi
  • Neidhardt, Hagen
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 47A40 47A55 47B44

Keywords

  • Feshbach decomposition, optical potential, Lax-Phillips scattering theory, dissipative scatteringtheory, scattering matrix, characteristicfunction, dissipative operators

Abstract

For an operator-valued block-matrix model, which is called in quantum physics a Feshbach decomposition, a scattering theory is considered. Under trace class perturbation the channel scattering matrices are calculated. Using Feshbach's optical potential it is shown that for a given spectral parameter the channel scattering matrices can be recovered either from a dissipative or from a Lax-Phillips scattering theory.

Appeared in

  • Operator Theory in Inner Product Spaces, K.-H. Förster, P. Jonas, H. Langer, C. Trunk, eds., Vol. 175 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2007, 33--49

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