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

Hideo TAMURA

doi:10.2969/jmsj/04310001

Hideo TAMURA

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 1 Pages 1-24

DOI https://doi.org/10.2969/jmsj/04310001

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Published: 1991 Received: September 22, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Amrein, A. M. Berthier and V. Georgescue, On Mourre's approach to spectral theory, Helv. Phys. Acta., 62 (1989), 1-20.
2) H. L. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts Monographs Phys., Springer-Verlag, 1987.
3) J. Derezinski, A new proof of the propagation theorem for N-body quantum systems, Commun. Math. Phys., 122 (1989), 203-231.
4) V. Enss, Quantum scattering theory for two- and three-body systems with potentials of short and long range, Schrödinger Operators, Lect. Notes in Math., 1159, Springer-Verlag, 1984.
5) R. Froese and I. Herbst, A new proof of the Mourre estimate, Duke Math. J., 49 (1982), 1075-1085.
6) T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1966), 258-279.
7) H. Kitada, On the completeness of N-body wave operators, University of Tokyo, Preprint, 1989.
8) E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Commun. Math. Phys., 78 (1981), 391-408.
9) P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann, of Math., 114 (1981), 519-567.
10) M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Scattering Theory, Academic Press, 1978.
11) I. M. Sigal and A. Soffer, The N-particle scattering problem, Asymptotic completeness for short-range systems, Ann. of Math., 125 (1987), 35-108.
12) H. Tamura, Principle of limiting absorption for N-body Schrödinger operators, A remark on the commutator method, Lett. In Math. Phys., 17 (1987), 31-36.

Right : [1] W. Amrein, A. M. Berthier and V. Georgescue, On Mourre's approach to spectral theory, Helv. Phys. Acta., 62 (1989), 1-20.
[2] H. L. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts Monographs Phys., Springer-Verlag, 1987.
[3] J. Derezinski, A new proof of the propagation theorem for N-body quantum systems, Commun. Math. Phys., 122 (1989), 203-231.
[4] V. Enss, Quantum scattering theory for two- and three-body systems with potentials of short and long range, Schrödinger Operators, Lect. Notes in Math., 1159, Springer-Verlag, 1984.
[5] R. Froese and I. Herbst, A new proof of the Mourre estimate, Duke Math. J., 49 (1982), 1075-1085.
[6] T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1966), 258-279.
[7] H. Kitada, On the completeness of N-body wave operators, University of Tokyo, Preprint, 1989.
[8] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Commun. Math. Phys., 78 (1981), 391-408.
[9] P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. of Math., 114 (1981), 519-567.
[10] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Scattering Theory, Academic Press, 1978.
[11] I. M. Sigal and A. Soffer, The N-particle scattering problem, Asymptotic completeness for short-range systems, Ann. of Math., 125 (1987), 35-108.
[12] H. Tamura, Principle of limiting absorption for N-body Schrödinger operators, A remark on the commutator method, Lett. In Math. Phys., 17 (1987), 31-36.

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