Advertisement

Communications in Mathematical Physics

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

The quasi-classical limit of quantum scattering theory

  • Kenji Yajima
Article

Abstract

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.

Keywords

Neural Network Asymptotic Behavior Nonlinear Dynamics Quantum Computing Scattering Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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 Unpublished note, ETH-Zürich (1974)Google Scholar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

Personalised recommendations