On the Decoupling of Finite Singularities from the Question of Asymptotic Completeness in Two Body Quantum Systems
نویسندگان
چکیده
Let V be a multiplication operator, whose negative part, V-(V-< 0) obeys-A + (1 + c)V->-c for some c, c > 0. Let W = Vx where x is the characteristic function of the exterior of a ball. Our main result asserts that the scattering for-A + V is complete if and only if that for-A + W is complete. Our technical estimates exploit Wiener integrals and the Feynman-Kac formula. We also make an application to acoustical scattering.
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