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- W2018013472 abstract "A theory of scattering for the time dependent evolution equations du dt = iH j (t)u, j = 0, 1 ( ∗ ) is developed. The wave operators are defined in terms of the evolution operators U j ( t , s ), which govern ( ∗ ). The scattering operator remains unitary. Sufficient conditions for existence and completeness of the wave operators are obtained; these are the main results. General properties, such as the chain rule and various intertwining relations, are also established. Applications include potential scattering ( H 0 ( t ) = − Δ , Δ denoting the Laplacian, and H 1 ( t ) = − Δ + q ( t , ·)) and scattering for second-order differential operators with coefficients constant in the spatial variable ( H j (t) = ∑ m, k = 1 n a mk (j) (t)( ∂ 2 ∂x m ∂x k ) + b j (t) for j = 0, 1 )." @default.
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- W2018013472 date "1974-07-01" @default.
- W2018013472 modified "2023-09-28" @default.
- W2018013472 title "Temporally inhomogeneous scattering theory" @default.
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- W2018013472 doi "https://doi.org/10.1016/0022-247x(74)90042-0" @default.
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