47A40 Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
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- 2008 (2)
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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.
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.