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

P. Deift; B. Simon

doi:10.1016/0022-1236(76)90049-5

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

P. Deift, B. Simon

Mathematics

Research output: Contribution to journal › Article › peer-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 = V_χ 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 language	English (US)
Pages (from-to)	218-238
Number of pages	21
Journal	Journal of Functional Analysis
Volume	23
Issue number	3
DOIs	https://doi.org/10.1016/0022-1236(76)90049-5
State	Published - Nov 1976

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(76)90049-5

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title = "On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems",

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.",

author = "P. Deift and B. Simon",

note = "Funding Information: * Research supported in part by AFOSR under Contract Number F44620-71-C-0108; Present address: Courant Institute, New York University. New York, New York. + A. Sloan Fellow; partially supported by the National Science Foundation under Grant Number GP-39048.",

year = "1976",

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AU - Deift, P.

AU - Simon, B.

N1 - Funding Information: * Research supported in part by AFOSR under Contract Number F44620-71-C-0108; Present address: Courant Institute, New York University. New York, New York. + A. Sloan Fellow; partially supported by the National Science Foundation under Grant Number GP-39048.

PY - 1976/11

Y1 - 1976/11

N2 - 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.

AB - 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.

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

Abstract

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