, Volume 61, Issue 2, pp 149-168

Local decay of scattering solutions to Schrödinger's equation

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Abstract

The main theorem asserts that ifH=Δ+gV is a Schrödinger Hamiltonian with short rangeV, φεL compact 2 (IR3), andR>0, then ‖exp(iHt 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).

Research supported by the National Science Foundation under grants NSF GP 34260 and MCS 72-05055 A04
Communicated by J. Ginibre