Representations of the Scattering Operator and the Scattering Amplitude, and Analyticity Properties of the Scattering Amplitude
Hellmut Baumgärtel, Manfred Wollenberg · Operator theory · 1983
Let Ŝ(λ) be the scattering matrix of a scattering system { H , H 0 ; J }. Then the operator function T̂(λ):= Ŝ(λ) − 1 ℋ λ is called the scattering amplitude . Its definition, like that of Ŝ(λ), depends on the special direct integral representation of P ac 0 ℋ 0 with respect to H 0 . A scattering system is called trivial if Ŝ(λ) = 1 ℋ λ for all λ ∈ ⊿ 0 = spec c ( H 0 | P ac 0 ℋ 0 ). The scattering amplitude Ŝ(λ) describes the deviation of the scattering system { H , H 0 ; J } from a trivial one. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.