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Asymptotic completeness for \(N\leq 4\) particle systems with the Coulomb-type interactions. (English) Zbl 0853.70010


MSC:

70F10 \(n\)-body problems
78A35 Motion of charged particles
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[1] H. Cycon, R. Froese, W. Kirsch, and B. Simon, Schrödinger Operators, with Application to Quantum Mechanics and Global Geometry , Texts and Monographs in Physics, Springer-Verlag, Berlin, 1987. · Zbl 0619.47005
[2] J.-M. Combes, Relatively compact interactions in many particle systems , Comm. Math. Phys. 12 (1969), 283-295. · Zbl 0174.28304
[3] V. Enss, Quantum scattering theory for two- and three-body systems with potentials of short- and long- range , Schrödinger Operators (Como, 1984) ed. S. Graffi, Lecture Notes in Math., vol. 1159, Springer-Verlag, Berlin, 1985, pp. 39-176. · Zbl 0585.35023
[4] G.-M. Graf, Asymptotic completeness for \(N\)-body short-range quantum systems: a new proof , Comm. Math. Phys. 132 (1990), no. 1, 73-101. · Zbl 0726.35096
[5] L. Hörmander, The Analysis of Linear Partial Differential Operators IV , Grundlehren Math. Wiss, vol. 275, Springer-Verlag, Berlin, 1985. · Zbl 0612.35001
[6] T. Kato, Fundamental properties of Hamiltonian operators of Schrödinger type , Trans. Amer. Math. Soc. 70 (1951), 195-211. JSTOR: · Zbl 0044.42701
[7] T. Kato, Wave operators and similarity for some non-selfadjoint operators , Math. Ann. 162 (1965/1966), 258-279. · Zbl 0139.31203
[8] H. Kitada, Asymptotic completeness of \(N\)-body wave operators I. Short-range quantum systems , Rev. Math. Phys. 3 (1991), no. 1, 101-124. · Zbl 0731.35076
[9] E. Mourre, Operateurs conjugués et propriétés de propagation , Comm. Math. Phys. 91 (1983), no. 2, 279-300. · Zbl 0543.47041
[10] P. Perry, Propagation of states in dilation analytic potentials and asymptotic completeness , Comm. Math. Phys. 81 (1981), no. 2, 243-259. · Zbl 0471.47007
[11] 1 M. Reed and B. Simon, Methods of Modern Mathematical Physics II. Fourier Analysis, Self-adjointness , Academic Press, New York, 1975. · Zbl 0308.47002
[12] 2 M. Reed and B. Simon, Methods of Modern Mathematical Physics III , Academic Press, New York, 1979. · Zbl 0405.47007
[13] I. M. Sigal, Mathematical questions of quantum many-body theory , Séminaire sur les équations aux dérivées partielles 1986-1987, École Polytech., Palaiseau, 1987, Exp. No. XXIII, 24. · Zbl 0656.35133
[14] I. M. Sigal, On long-range scattering , Duke Math. J. 60 (1990), no. 2, 473-496. · Zbl 0725.35071
[15] I. M. Sigal and A. Soffer, The \(N\)-particle scattering problem: asymptotic completeness for short-range systems , Ann. of Math. (2) 126 (1987), no. 1, 35-108. JSTOR: · Zbl 0646.47009
[16] I. M. Sigal and A. Soffer, Asymptotic completeness of multiparticle scattering , Differential Equations and Mathematical Physics (Birmingham, Ala., 1986) eds. I. W. Knowles and Y. Saito, Lecture Notes in Math., vol. 1285, Springer-Verlag, Berlin, 1987, pp. 435-472. · Zbl 0651.35071
[17] I. M. Sigal and A. Soffer, Long-range many-body scattering. Asymptotic clustering for Coulomb-type potentials , Invent. Math. 99 (1990), no. 1, 115-143. · Zbl 0702.35197
[18] I. M. Sigal and A. Soffer, Local decay and velocity bounds ,
[19] I. M. Sigal and A. Soffer, Asymptotic completeness for Coulomb-type \(3\)-body systems , preprint, Princeton Univ, 1991. · Zbl 0853.70010
[20] A. G. Sigalov and I. M. Sigal, Description of the spectrum of the energy operator of quantum mechanical systems , Theoret. and Math. Phys. 5 (1970), 990-1005.
[21] K. Sinha and Pl. Muthuramalingam, Asymptotic evolution of certain observables and completeness in Coulomb scattering I , J. Funct. Anal. 55 (1984), no. 3, 323-343. · Zbl 0531.47008
[22] H. Tamura, Propagation estimate for \(N\)-body quantum systems , Bull. Fac. Sci. Ibaraki Univ. Ser. A 22 (1990), 29-48. · Zbl 0751.47037
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