On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems

P. Deift, B. Simon

Research output: Contribution to journalArticlepeer-review

Abstract

Let V be a multiplication operator, whose negative part, V-(V- ≤ 0) obeys - Δ + (1 + ε{lunate})V- ≥ -c for some ε{lunate}, c > 0. Let W = Vχ where χ is the characteristic function of the exterior of a ball. Our main result asserts that the scattering for - Δ + V is complete if and only if that for - Δ + W is complete. Our technical estimates exploit Wiener integrals and the Feynman-Kac formula. We also make an application to acoustical scattering.

Original languageEnglish (US)
Pages (from-to)218-238
Number of pages21
JournalJournal of Functional Analysis
Volume23
Issue number3
DOIs
StatePublished - Nov 1976

ASJC Scopus subject areas

  • Analysis

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