On the wave operators and Levinson’s theorem for potential scattering in R
نویسنده
چکیده
The paper is a presentation of recent investigations on potential scattering in R. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. A topological version of Levinson’s theorem is proposed by interpreting it as an index theorem.
منابع مشابه
ar X iv : 0 80 8 . 15 64 v 1 [ m at h - ph ] 1 1 A ug 2 00 8 On the structure of the wave operators in one dimensional potential scattering
In the framework of one dimensional potential scattering we prove that, modulo a compact term, the wave operators can be written in terms of a universal operator and of the scattering operator. The universal operator is related to the one dimensional Hilbert transform and can be expressed as a function of the generator of dilations. As a consequence, we show how Levinson’s theorem can be rewrit...
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