Short-range interactions. asymptotic completeness

We consider an N-body quantum system in a constant magnetic field which consists of just one charged and the other N - 1 neutral particles. We prove the existence of a conjugate operator for the Hamiltonian which governs the system, and show the asymptotic completeness of the system under short-range assumptions on the pair potentials.

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ASYMPTOTIC COMPLETENESS OF N-BODY WAVE OPERATORS I: SHORT-RANGE QUANTUM SYSTEMS

Reviews in Mathematical Physics ◽

10.1142/s0129055x91000047 ◽

1991 ◽

Vol 03 (01) ◽

pp. 101-124 ◽

Cited By ~ 23

Author(s):

HITOSHI KITADA

Keyword(s):

Short Range ◽

Body Wave ◽

Asymptotic Completeness ◽

Quantum Systems ◽

Wave Operators

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Asymptotic completeness of N-body wave operators II. A new proof for the short-range case and the asymptotic clustering for long-range systems

Lecture Notes in Mathematics - Functional Analysis and Related Topics, 1991 ◽

10.1007/bfb0085479 ◽

1993 ◽

pp. 149-189 ◽

Cited By ~ 2

Author(s):

Hitoshi Kitada

Keyword(s):

Long Range ◽

Short Range ◽

Body Wave ◽

Asymptotic Completeness ◽

Wave Operators

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Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces

Methods and Applications of Analysis ◽

10.4310/maa.2007.v14.n3.a3 ◽

2007 ◽

Vol 14 (3) ◽

pp. 251-262 ◽

Cited By ~ 4

Author(s):

Seung-Yeal Ha ◽

Yong Duck Kim ◽

Ho Lee ◽

Se Eun Noh

Keyword(s):

Short Range ◽

Kinetic Equations ◽

Asymptotic Completeness ◽

Short Range Interaction ◽

Range Interaction ◽

Interaction Forces

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Asymptotic completeness for four-body Schrödinger operators with short-range interactions

Publications of the Research Institute for Mathematical Sciences ◽

10.2977/prims/1195167541 ◽

1993 ◽

Vol 29 (1) ◽

pp. 1-21 ◽

Cited By ~ 1

Author(s):

Hideo Tamura

Keyword(s):

Short Range ◽

Schrödinger Operators ◽

Asymptotic Completeness ◽

Schrodinger Operators

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Asymptotic completeness of many-body short-range systems

Letters in Mathematical Physics ◽

10.1007/bf00402233 ◽

1984 ◽

Vol 8 (3) ◽

pp. 181-188 ◽

Cited By ~ 3

Author(s):

I. M. Sigal

Keyword(s):

Short Range ◽

Asymptotic Completeness ◽

Many Body

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Asymptotic completeness of short-range many-body systems

Bulletin of the American Mathematical Society ◽

10.1090/s0273-0979-1986-15408-x ◽

1986 ◽

Vol 14 (1) ◽

pp. 107-111 ◽

Cited By ~ 4

Author(s):

I. M. Sigal ◽

A. Soffer

Keyword(s):

Short Range ◽

Asymptotic Completeness ◽

Many Body ◽

Many Body Systems

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Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: Möller Wave Operators and Asymptotic Completeness

Lecture Notes in Applied Differential Equations of Mathematical Physics ◽

10.1142/9789812814586_0002 ◽

2008 ◽

pp. 39-57

Keyword(s):

Quantum Mechanics ◽

Scattering Theory ◽

Short Range ◽

Asymptotic Completeness ◽

Wave Operators

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Asymptotic completeness for a quantum particle in a Markovian short range potential

Communications in Mathematical Physics ◽

10.1007/bf01211102 ◽

1986 ◽

Vol 105 (2) ◽

pp. 259-280 ◽

Cited By ~ 13

Author(s):

Claude-Alain Pillet

Keyword(s):

Short Range ◽

Quantum Particle ◽

Asymptotic Completeness ◽

Short Range Potential ◽

Range Potential

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Asymptotic completeness for three-body Schrödinger operators with short-range interactions

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/04310001 ◽

1991 ◽

Vol 43 (1) ◽

pp. 1-24

Author(s):

Hideo TAMURA

Keyword(s):

Short Range ◽

Schrödinger Operators ◽

Asymptotic Completeness ◽

Schrodinger Operators ◽

Three Body

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