Asymptotic completeness of certain four-body Schrödinger operators

George A. Hagedorn; Peter A. Perry

doi:10.1016/0022-1236(86)90008-X

Asymptotic completeness of certain four-body Schrödinger operators

George A. Hagedorn, Peter A. Perry

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We give a proof of asymptotic completeness for four-body Schrödinger operators. The two-body potentials are assumed to be short range and there are spectral assumptions on the two- and three-body subsystems. These spectral assumptions hold generically for certain classes of potentials. The proof of the main theorem depends on an analysis of the rates of decay of the wave function in certain regions of configuration space, depending on the scattering channel to which the wave function belongs.

Original language	English
Pages (from-to)	172-203
Number of pages	32
Journal	Journal of Functional Analysis
Volume	65
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(86)90008-X
State	Published - Feb 1 1986

Bibliographical note

Funding Information:
*The material is partly based on work supported by the National Science Foundation under grants MCS-8100738 and MCS-8301277. + Bantrell Fellow in Mathematical Physics. Present address: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506.

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/0022-1236(86)90008-X

Cite this

@article{47869bcca0ca4190ac3dd61e418d749a,

title = "Asymptotic completeness of certain four-body Schr{\"o}dinger operators",

abstract = "We give a proof of asymptotic completeness for four-body Schr{\"o}dinger operators. The two-body potentials are assumed to be short range and there are spectral assumptions on the two- and three-body subsystems. These spectral assumptions hold generically for certain classes of potentials. The proof of the main theorem depends on an analysis of the rates of decay of the wave function in certain regions of configuration space, depending on the scattering channel to which the wave function belongs.",

author = "Hagedorn, {George A.} and Perry, {Peter A.}",

note = "Funding Information: *The material is partly based on work supported by the National Science Foundation under grants MCS-8100738 and MCS-8301277. + Bantrell Fellow in Mathematical Physics. Present address: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506.",

year = "1986",

month = feb,

day = "1",

doi = "10.1016/0022-1236(86)90008-X",

language = "English",

volume = "65",

pages = "172--203",

number = "2",

}

TY - JOUR

T1 - Asymptotic completeness of certain four-body Schrödinger operators

AU - Hagedorn, George A.

AU - Perry, Peter A.

N1 - Funding Information: *The material is partly based on work supported by the National Science Foundation under grants MCS-8100738 and MCS-8301277. + Bantrell Fellow in Mathematical Physics. Present address: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506.

PY - 1986/2/1

Y1 - 1986/2/1

N2 - We give a proof of asymptotic completeness for four-body Schrödinger operators. The two-body potentials are assumed to be short range and there are spectral assumptions on the two- and three-body subsystems. These spectral assumptions hold generically for certain classes of potentials. The proof of the main theorem depends on an analysis of the rates of decay of the wave function in certain regions of configuration space, depending on the scattering channel to which the wave function belongs.

AB - We give a proof of asymptotic completeness for four-body Schrödinger operators. The two-body potentials are assumed to be short range and there are spectral assumptions on the two- and three-body subsystems. These spectral assumptions hold generically for certain classes of potentials. The proof of the main theorem depends on an analysis of the rates of decay of the wave function in certain regions of configuration space, depending on the scattering channel to which the wave function belongs.

UR - http://www.scopus.com/inward/record.url?scp=46149135056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46149135056&partnerID=8YFLogxK

U2 - 10.1016/0022-1236(86)90008-X

DO - 10.1016/0022-1236(86)90008-X

M3 - Article

AN - SCOPUS:46149135056

SN - 0022-1236

VL - 65

SP - 172

EP - 203

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Asymptotic completeness of certain four-body Schrödinger operators

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this