New channels of scattering for three-body quantum systems with long-range potentials
Dimitri Yafaev
Source: Duke Math. J. Volume 82, Number 3
(1996), 553-584.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245252
Mathematical Reviews number (MathSciNet): MR1387684
Zentralblatt MATH identifier: 0859.35084
Digital Object Identifier: doi:10.1215/S0012-7094-96-08223-X
References
[1] L. Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR87d:35002b
Zentralblatt MATH: 0612.35001
[2] L. D. Faddeev, Mathematical aspects of the three-body problem in quantum scattering theory, Trudy Mat. Inst. Steklov. 69 (1963), (in Russian); English translation by Ch. Gutfreund, Daniel Davey & Co., Inc., New York, 1965.
Mathematical Reviews (MathSciNet): MR221828
Zentralblatt MATH: 0131.43504
[3] V. Enss, Completeness of three-body quantum scattering, Dynamics and processes (Bielefeld, 1981), Lecture Notes in Math., vol. 1031, Springer, Berlin, 1983, pp. 62–88.
Mathematical Reviews (MathSciNet): MR85h:81071
Zentralblatt MATH: 0531.47009
Digital Object Identifier: doi:10.1007/BFb0072111
[4] V. Enss, Quantum scattering theory for two- and three-body systems with potentials of short and long range, Schrödinger operators (Como, 1984), Lecture Notes in Math., vol. 1159, Springer, Berlin, 1985, pp. 39–176.
Mathematical Reviews (MathSciNet): MR87c:81169
Zentralblatt MATH: 0585.35023
[5] V. Enss, Long-range scattering of two- and three-body quantum systems, Journées “Équations aux Dérivées Partielles” (Saint Jean de Monts, 1989), École Polytech., Palaiseau, 1989, p. 31.
Mathematical Reviews (MathSciNet): MR91a:81214
Zentralblatt MATH: 0734.35069
[6] X. P. Wang, On the three-body long-range scattering problems, Lett. Math. Phys. 25 (1992), no. 4, 267–276.
Mathematical Reviews (MathSciNet): MR93i:81287
Zentralblatt MATH: 0776.35045
Digital Object Identifier: doi:10.1007/BF00398399
[7] C. Gérard, Asymptotic completeness for $3$-particle long-range systems, Invent. Math. 114 (1993), no. 2, 333–397.
Mathematical Reviews (MathSciNet): MR94f:81171
Zentralblatt MATH: 0812.70006
Digital Object Identifier: doi:10.1007/BF01232674
[8] J. Dereziński, Asymptotic completeness of long-range $N$-body quantum systems, Ann. of Math. (2) 138 (1993), no. 2, 427–476.
Mathematical Reviews (MathSciNet): MR94g:81209
Zentralblatt MATH: 0844.47005
Digital Object Identifier: doi:10.2307/2946615
JSTOR: links.jstor.org
[9] D. R. Yafaev, On the break-down of completeness of wave operators in potential scattering, Comm. Math. Phys. 65 (1979), no. 2, 167–179.
Mathematical Reviews (MathSciNet): MR82j:35118
Zentralblatt MATH: 0401.47006
Digital Object Identifier: doi:10.1007/BF01225147
Project Euclid: euclid.cmp/1103904829
[10] D. R. Yafaev, New channels in two-body long-range scattering, to appear in Algebra and Analysis 8, 1996.
[11] D. R. Jafaev, Wave operators for the Schrödinger equation, Teoret. Mat. Fiz. 45 (1980), no. 2, 224–234, in Russian.
Mathematical Reviews (MathSciNet): MR82j:35119
Zentralblatt MATH: 0458.35078
[12] J. Dollard, Asymptotic convergence and the Coulomb interaction, J. Mathematical Phys. 5 (1964), 729–738.
Mathematical Reviews (MathSciNet): MR29:921
Digital Object Identifier: doi:10.1063/1.1704171
[13] V. S. Buslaev and V. B. Matveev, Wave operators for the Schrödinger equation with slowly decreasing potential, Teoret. Mat. Fiz. 2 (1970), no. 3, 367–376.
Mathematical Reviews (MathSciNet): MR57:13246
[14] D. R. Yafaev, The low energy scattering for slowly decreasing potentials, Comm. Math. Phys. 85 (1982), no. 2, 177–196.
Mathematical Reviews (MathSciNet): MR84g:34047
Zentralblatt MATH: 0509.35065
Digital Object Identifier: doi:10.1007/BF01254456
Project Euclid: euclid.cmp/1103921410
[15] M. S. Ashbaugh and E. M. Harrell, Perturbation theory for shape resonances and large barrier potentials, Comm. Math. Phys. 83 (1982), no. 2, 151–170.
Mathematical Reviews (MathSciNet): MR84j:81027
Zentralblatt MATH: 0494.34044
Digital Object Identifier: doi:10.1007/BF01976039
Project Euclid: euclid.cmp/1103920799
Duke Mathematical Journal
