We prove new formulae for the wave operators for a Friedrichs scattering system with a rank one perturbation, and we derive a topological version of Levinson's theorem for this model.
On the wave operators and Levinson's theorem for potential scattering in R^3
Discrete Laplacian in a half-space with a periodic surface potential I: Resolvent expansions, scattering matrix, and wave operators
Remarks on $L^p$-boundedness of wave operators for Schrödinger operators with threshold singularities
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