Abstract
Scattering theory for time dependent HamiltonianH(t)=−(1/2) Δ+ΣV j (x−q j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V j (x)|≦C j (1+|x|)−2−ε, roughly spoken; and the trajectoriesq j (t) are straight lines at remote past and far future, and |q j (t)−q k (t)| → ∞ ast → ± ∞ (j≠k).
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Communicated by B. Simon
Partly supported by Sakkô-kai Foundation.
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Yajima, K. A multi-channel scattering theory for some time dependent Hamiltonians, charge transfer problem. Commun.Math. Phys. 75, 153–178 (1980). https://doi.org/10.1007/BF01222515
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DOI: https://doi.org/10.1007/BF01222515