Hagedorn, George A. Asymptotic completeness for the impact parameter approximation to three particle scattering. (English) Zbl 0482.47003 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 36, 19-40 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 9 Documents MSC: 47A40 Scattering theory of linear operators 70F07 Three-body problems Keywords:impact parameter approximation; three body scattering problem; time dependent Schrödinger equation; scattering amplitudes; Faddeev-Watson multiple collision series × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] S. Agmon , Spectral Properties of Schrödinger Operators and Scattering Theory . Ann. Scuola Norm. Sup. Pisa , t. 2 , 1975 , p. 151 - 218 . Numdam | MR 397194 | Zbl 0315.47007 · Zbl 0315.47007 [2] L.D. Faddeev , Mathematical Aspects of the Three-body Problem in the Quantum Scattering Theory Israel Program for Scientific Translations , Jérusalem , 1965 . MR 221828 | Zbl 0131.43504 · Zbl 0131.43504 [3] J. Ginibre , M. Moulin , Hilbert Space Approach to the Quantum Mechanical Three Body Problem , Ann. Inst. H. Poincaré , Sect. A , 21 , 1974 , p. 97 - 145 . Numdam | MR 368656 | Zbl 0311.47003 · Zbl 0311.47003 [4] R.R. Goldberg , Fourier Transforms , London , Cambridge , University, Presse , 1962 . MR 120501 | Zbl 0095.08601 · Zbl 0095.08601 [5] G.A. Hagedorn , Asymptotic Completeness for Classes of Two, Three, and Four Particle Schrödinger Operators . Trans. Amer. Math. Soc. , t. 258 , 1980 , p. 1 - 75 . MR 554318 | Zbl 0428.47004 · Zbl 0428.47004 · doi:10.2307/1998280 [6] G.A. Hagedorn , Born Series for (2 Cluster) \rightarrow (2 Cluster) Scattering of Two, Three, and Four Particle Schrödinger Operators . Comm. Math. Phys. , t. 66 , 1979 , p. 77 - 94 . Article | MR 530916 | Zbl 0418.47003 · Zbl 0418.47003 · doi:10.1007/BF01197746 [7] J.S. Howland , Stationary Scattering Theory and Time-dependent Hamiltonians . Math. Ann. , t. 207 , 1974 , p. 315 - 335 . MR 346559 | Zbl 0261.35067 · Zbl 0261.35067 · doi:10.1007/BF01351346 [8] J.S. Howland , Abstract Stationary Theory of Multichannel Scattering . J. Functional Analysis , t. 22 , 1976 , p. 250 - 282 . MR 461175 | Zbl 0327.47004 · Zbl 0327.47004 · doi:10.1016/0022-1236(76)90012-4 [9] R. Paley , N. Wiener , Fourier Transforms in the Complex Domain , Amer. Math. Soc. Colloquium Publication , Providence, RI , 1934 . MR 1451142 | Zbl 0011.01601 | JFM 60.0345.02 · Zbl 0011.01601 [10] M. Reed , B. Simon , Methods of Modern Mathematical Physics , Vol. II , Fourier Analysis, Self-adjointness , New York , London , Academic Press , 1975 . Zbl 0308.47002 · Zbl 0308.47002 [11] M. Reed , B. Simon , Methods of Modern Mathematical Physics , Vol. IV , Analysis of Operators , New York , London , Academic press , 1978 . Zbl 0401.47001 · Zbl 0401.47001 [12] R. Shakeshaft , L. Spruch , Mechanisms for Charge Transfer ( or the Capture of any Light Particle ) at Asymptotically High impact Velocities . Rev. Mod. Phys. , t. 51 , 1979 , p. 369 - 406 . [13] C.S. Shastri , A.K. Rajagopal , J. Callaway , Coulomb T-Matrix and the Proton-Hydrogen Charge Exchange ., Phys. Rev. , t. A 6 , 1972 , p. 268 - 278 . [14] B. Simon , Quantum Mechanics for Hamiltonians Defined as Quadratic Forms . Princeton University, Press , 1971 . MR 455975 | Zbl 0232.47053 · Zbl 0232.47053 [15] B. Simon , Geometric Methods in Multiparticle Quantum Systems . Comm. Math. Phys. , t. 55 , 1977 , p. 259 - 274 . Article | MR 496073 | Zbl 0413.47008 · Zbl 0413.47008 · doi:10.1007/BF01614550 [16] L.E. Thomas , Asymptotic Completeness in Two- and Three-Particle Quantum Mechanical Scattering . Ann. Phys. , t. 90 , 1975 , p. 127 - 165 . MR 424082 [17] S. Weinberg , Systematic Solution of Multiparticle Scattering Problems . Phys. Rev. , t. B 133 , 1964 , p. 232 - 256 . MR 165883 [18] K. Yajima , A Multi-Channel Scattering Theory for some Time Dependent Hamiltonians , Charge Transfer Problem. Comm. Math. Phys. , t. 75 , 1980 , p. 153 - 178 . Article | MR 582506 | Zbl 0437.47008 · Zbl 0437.47008 · doi:10.1007/BF01222515 [19] K. Yosida , Functional Analysis , Berlin , Heidelberg , New York , Springer Verlag , 1968 . MR 617913 · Zbl 0152.32102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.