Asymptotic completeness for the impact parameter approximation to three particle scattering

George A. Hagedorn

Annales de l'I.H.P. Physique théorique (1982)

  • Volume: 36, Issue: 1, page 19-40
  • ISSN: 0246-0211

How to cite

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Hagedorn, George A.. "Asymptotic completeness for the impact parameter approximation to three particle scattering." Annales de l'I.H.P. Physique théorique 36.1 (1982): 19-40. <http://eudml.org/doc/76145>.

@article{Hagedorn1982,
author = {Hagedorn, George A.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {impact parameter approximation; three body scattering problem; time dependent Schrödinger equation; scattering amplitudes; Faddeev-Watson multiple collision series},
language = {eng},
number = {1},
pages = {19-40},
publisher = {Gauthier-Villars},
title = {Asymptotic completeness for the impact parameter approximation to three particle scattering},
url = {http://eudml.org/doc/76145},
volume = {36},
year = {1982},
}

TY - JOUR
AU - Hagedorn, George A.
TI - Asymptotic completeness for the impact parameter approximation to three particle scattering
JO - Annales de l'I.H.P. Physique théorique
PY - 1982
PB - Gauthier-Villars
VL - 36
IS - 1
SP - 19
EP - 40
LA - eng
KW - impact parameter approximation; three body scattering problem; time dependent Schrödinger equation; scattering amplitudes; Faddeev-Watson multiple collision series
UR - http://eudml.org/doc/76145
ER -

References

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  2. [2] L.D. Faddeev, Mathematical Aspects of the Three-body Problem in the Quantum Scattering Theory Israel Program for Scientific Translations, Jérusalem, 1965. Zbl0131.43504MR221828
  3. [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. Zbl0311.47003MR368656
  4. [4] R.R. Goldberg, Fourier Transforms, London, Cambridge, University, Presse, 1962. Zbl0095.08601MR120501
  5. [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. Zbl0428.47004MR554318
  6. [6] G.A. Hagedorn, Born Series for (2 Cluster) → (2 Cluster) Scattering of Two, Three, and Four Particle Schrödinger Operators. Comm. Math. Phys., t. 66, 1979, p. 77-94. Zbl0418.47003MR530916
  7. [7] J.S. Howland, Stationary Scattering Theory and Time-dependent Hamiltonians. Math. Ann., t. 207, 1974, p. 315-335. Zbl0261.35067MR346559
  8. [8] J.S. Howland, Abstract Stationary Theory of Multichannel Scattering. J. Functional Analysis, t. 22, 1976, p. 250-282. Zbl0327.47004MR461175
  9. [9] R. Paley, N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc.Colloquium Publication, Providence, RI, 1934. Zbl0011.01601MR1451142JFM60.0345.02
  10. [10] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. II, Fourier Analysis, Self-adjointness, New York, London, Academic Press, 1975. Zbl0308.47002
  11. [11] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. IV, Analysis of Operators, New York, London, Academic press, 1978. Zbl0401.47001
  12. [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. [13] C.S. Shastri, A.K. Rajagopal, J. Callaway, Coulomb T-Matrix and the Proton-Hydrogen Charge Exchange., Phys. Rev., t. A6, 1972, p. 268-278. 
  14. [14] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton University, Press, 1971. Zbl0232.47053MR455975
  15. [15] B. Simon, Geometric Methods in Multiparticle Quantum Systems. Comm. Math. Phys., t. 55, 1977, p. 259-274. Zbl0413.47008MR496073
  16. [16] L.E. Thomas, Asymptotic Completeness in Two- and Three-Particle Quantum Mechanical Scattering. Ann. Phys., t. 90, 1975, p. 127-165. MR424082
  17. [17] S. Weinberg, Systematic Solution of Multiparticle Scattering Problems. Phys. Rev., t. B133, 1964, p. 232-256. MR165883
  18. [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. Zbl0437.47008MR582506
  19. [19] K. Yosida, Functional Analysis, Berlin, Heidelberg, New York, Springer Verlag, 1968. Zbl0152.32102MR617913

Citations in EuDML Documents

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  1. Lech Zielinski, Complétude asymptotique pour un modèle du transfert de charge
  2. George A. Hagedorn, An analog of the RAGE theorem for the impact parameter approximation to three particle scattering
  3. George A. Hagedorn, Analysis of a nontrivial, explicitly solvable multichannel scattering system
  4. Galina Perelman, Asymptotic stability of solitary waves for nonlinear Schrödinger equations
  5. Lech Zielinski, Scattering for a dispersive charge transfer model
  6. Lech Zieliński, Charge transfer scatteringin a constant electric field

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