Abstract.
The paper is devoted to Schrödinger operators with dissipative boundary conditions on bounded intervals. 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 Schrödinger-Poisson systems.
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In friendship dedicated to P. Exner on the occasion of his 60th birthday
This work was supported by DFG, Grant 1480/2.
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Neidhardt, H., Rehberg, J. Scattering Matrix, Phase Shift, Spectral Shift and Trace Formula for One-dimensional Dissipative Schrödinger-type Operators. Integr. equ. oper. theory 58, 407–431 (2007). https://doi.org/10.1007/s00020-007-1487-z
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DOI: https://doi.org/10.1007/s00020-007-1487-z