Communications in Mathematical Physics

, Volume 69, Issue 2, pp 101–129 | Cite as

The quasi-classical limit of quantum scattering theory

  • Kenji Yajima


We study the quasi-classical limit of the quantum mechanical scattering operator for non-relativistic simple scattering system. The connection between the quantum mechanical and classical mechanical scattering theories is obtained by considering the asymptotic behavior as ħ → 0 of the quantum mechanical scattering operator on the state exp(—ip·a/ħ)f(p) in the momentum representation.


Neural Network Asymptotic Behavior Nonlinear Dynamics Quantum Computing Scattering Theory 
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  1. 1.
    Agmon, S.: Spectral Properties of Schrödinger operators and scattering theory. Ann. Scuola Nor. Pisa, Ser IV,2.2, 151–218 (1975)Google Scholar
  2. 2.
    Asada, K., Fujiwara, D.: On some oscillatory integral transformations in L2 (ℝn). Jpn. J. Math.4, 299–361 (1978)Google Scholar
  3. 3.
    Fujiwara, D.: A construction of the fundamental solution for Schrödinger equation. J. d'Analyse Math. (In press)Google Scholar
  4. 4.
    Hepp, K.: The classical limit for quantum mechanical correlation functions. Commun. Math. Phys.35, 265–277 (1974)Google Scholar
  5. 5.
    Hepp, K.: On the classical limit in Quantum mechanics. Unpublished note, ETH-Zürich (1974)Google Scholar
  6. 6.
    Herbst, W.: Classical scattering with long range forces. Commun. Math. Phys.35, 193–214 (1974)Google Scholar
  7. 7.
    Hörmander, L.: Fourier integral operators. Acta. Math.127, 79–183 (1971)Google Scholar
  8. 8.
    Hörmander, L.: The existence of wave operators in scattering theory. Math. Z.146, 69–91 (1976)Google Scholar
  9. 9.
    Hunziker, W.: The S-matrix in classical mechanics. Commun. Math. Phys.,8, 283–299 (1968)Google Scholar
  10. 10.
    Kuroda, S. T.: Scattering theory for differential operators. J. Math. Soc. Japan25, 75–104 (1973)Google Scholar
  11. 11.
    Maslov, V.P.: Théorie des perturbations et méthodes asymptotiques (Translation from Russian) Paris: Dunod 1972Google Scholar
  12. 12.
    Simon, B.: Wave operators for classical particle scattering. Commun. Math. Phys.23, 37–48 (1971)Google Scholar
  13. 13.
    Dollard, J. D.: Scattering into cones. I. Potential scattering. Commun. Math. Phys.12, 193–203 (1969)Google Scholar
  14. 14.
    Yajima, K.: The quasi-classical limit of quantum scattering theory. II. Long range scattering. Preprint, University of Virginia (1978)Google Scholar
  15. 15.
    Landau, L. D., Lifschitz, E. M.: Course of theoretical physics, Vol. 1, Mechanics (Translation from Russian). New York: Pergamon Press 1969.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Kenji Yajima
    • 1
    • 2
  1. 1.Mathematical Research InstituteETH-ZürichSwitzerland
  2. 2.Department of MathematicsUniversity of TokyoTokyoJapan

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