H. Neidhardt, J. Rehberg
Scattering matrix, phase shift, spectral shift and trace 
formula for one-dimensional dissipative Schr\"odinger-type operators
(400K, pdf)

ABSTRACT.  The paper is devoted to 
Schr\"odinger 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, the trace 
formula and the Birman-Krein formula are verified directly. The results 
are exploited for dissipative Schr\"odinger-Poisson systems.