Abstract
The main theorem asserts that ifH=Δ+gV is a Schrödinger Hamiltonian with short rangeV, φεL 2compact (IR3), andR>0, then ‖exp(iHt)Π S φ‖ L 2 (|x|<R)=O(t −1/2), ast→∞ where Π S is projection onto the orthogonal complement of the real eigenvectors ofH. For all but a discrete set ofg,O(t −1/2) may be replaced byO(t −3/2).
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Communicated by J. Ginibre
Research supported by the National Science Foundation under grants NSF GP 34260 and MCS 72-05055 A04
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Rauch, J. Local decay of scattering solutions to Schrödinger's equation. Commun.Math. Phys. 61, 149–168 (1978). https://doi.org/10.1007/BF01609491
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DOI: https://doi.org/10.1007/BF01609491