Asymptotic completeness for the impact parameter approximation to three particle scattering. (English) Zbl 0482.47003
Keywords:
impact parameter approximation; three body scattering problem; time dependent Schrödinger equation; scattering amplitudes; Faddeev-Watson multiple collision seriesReferences:
| [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 |
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