Abstract
We outline a time-dependent proof of asymptotic completeness for scattering of three quantum mechanical particles which may be distinguishable or identical. The particles interact with pair potentials of short range, i.e. roughly with decay like r-1-ε, ε>0 towards infinity. In particular the two body subsystems may have bound states or resonances at zero energy, and the three body system may have infinitely many scattering channels. The dimension is arbitrary.
Keywords
- Wave Operator
- Asymptotic Completeness
- Spectral Subspace
- Smooth Cutoff Function
- Singular Continuous Spectrum
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References
W.O. Amrein and V. Georgescu, Helv. Phys. Acta 46, 635–658(1973).
W.O. Amrein, D.B. Pearson, M. Wollenberg, Helv. Phys. Acta 53, 335–351 (1980).
E.B. Davies, Duke Math. J. 47, 171–185(1980).
V. Enss, Commun. Math. Phys. 61, 285–291 (1978).
-, Ann. Phys. (N.Y.) 119, 117–132 (1979).
-, Commun. Math. Phys. 65, 151–165 (1979).
-: Geometric methods in spectral and scattering theory of Schrödinger operators, in: Rigorous Atomic and Molecular Physics, G. Velo, A.S. Wightman eds., Plenum, New York 1981.
-, Acta Physica Austriaca, Suppl. 23, 29–63(1981).
-: Asymptotic observables on scattering states, preprint Dept. Math. Univ. Bochum, in preparation
-: Propagation properties of quantum scattering states, preprint Institut Mittag-Leffler, Djursholm, 1982
-: Three Body Quantum Scattering Theory, preprint Dept. Math. Univ. Bochum, in preparation.
L.D. Faddeev: Mathematical Aspects of the Three Body Problem in Quantum Scattering Theory, Israel Program for Scientific Translations, 1965.
J. Ginibre: La méthode "dépendant du temps" dans le problème de la complétude asymptotique, preprint Univ. Paris-Sud, LPTHE 80/10, 1980.
J. Ginibre and M. Moulin, Ann. Inst. H. Poincaré A 21, 97–145(1974).
S.P. Merkuriev: Acta Physica Austriaca, Suppl. 23, 65–110(1981) and references given there.
E. Mourre, Commun. Math. Phys. 68, 91–94(1979).
-, Commun. Math. Phys. 78, 391–408 (1981).
P.A. Perry, Duke Math. J. 47, 187–193(1980).
P.A. Perry, I. Sigal, and B. Simon, Ann. Math. 114, 519–567(1981).
M. Reed and B. Simon: Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, New York 1979.
-:-, IV. Analysis of Operators, Academic Press, New York, 1978.
D. Ruelle, Nuovo Cimento 61 A, 655–662(1969).
B. Simon, Duke Math. J. 46, 119–168(1979).
D.R. Yafaev: On the proof of Enss of asymptotic completeness in potential scattering theory, to appear in Mathematics of the USSR, Sbornik.
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© 1983 Springer-Verlag
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Enss, V. (1983). Completeness of three body quantum scattering. In: Blanchard, P., Streit, L. (eds) Dynamics and Processes. Lecture Notes in Mathematics, vol 1031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072111
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DOI: https://doi.org/10.1007/BFb0072111
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