Advertisement

Random Media pp 163-182 | Cite as

Some Recent Results on Wave Equations, Path Integrals, and Semiclassical Approximations

  • John R. Klauder
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 7)

Abstract

Following a review of standard semiclassical approximations to wave equations in the configuration-space formulation, an approach based on a coherent-state representation is fully developed. Unlike direct configuration-space approaches, it is shown that the coherent-state formulation leads to a global, uniform, semiclassical configuration-space approximation, which has distinct advantages when one is faced with numerous caustics.

Keywords

Wave Equation Path Integral Random Medium Classical Trajectory Extremal Solution 
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.
    See, e.g., L. Schulman, Techniques and Applications of Path Integration ( Wiley Sons, New York, 1981 ).MATHGoogle Scholar
  2. 2.
    V. P. Maslov, Thèorie des Perturbations et Méthodes Asymptotiques ( Dunod, Paris, 1972 ).MATHGoogle Scholar
  3. 3.
    R. G. Littlejohn, Phys. Rev. Letters 54, 1742 (1985).Google Scholar
  4. 4.
    See, e.g., J. R. Klauder, B.-S. Skagerstam, Coherent States ( World Scientific, Singapore, 1985 ).MATHGoogle Scholar
  5. 5.
    J. R. Klauder, I. Daubechies, Phys. Rev. Letters 52, 1161 (1984)MathSciNetCrossRefGoogle Scholar
  6. I. Daubechies, J. R. Klauder, J. Math. Phys. 26, 2239 (1985).MathSciNetMATHCrossRefGoogle Scholar
  7. 6.
    See, e.g., R. S. Brodkey, The Phenomena of Fluid Motions (Addison-Wesley, Reading, Mass., 1967), Chap. 9.Google Scholar
  8. 7.
    J. R. Klauder, in Path Integrals and their Applications in Quantum, Statistical and Solid-State Physics, eds. G. J. Papadopoulis, J. T. Devreese (Plenum, New York, 1978), p. 5; Phys. Rev. D19, 2349 (1978); in Quantum Fields-Algebras, Processes, ed. L. Streit ( Springer, Vienna, 1980 ), p. 65.Google Scholar
  9. 8.
    J. R. Klauder, “Path Integrals and Semiclassical Approximations to Wave Equations,” (ATT Bell Laboratories preprint).Google Scholar
  10. 9.
    An announcement of this result appears in J. R. Klauder, “Global, Uniform, Semiclassical Approximation to Wave Equations,” (ATT Bell Laboratories preprint).Google Scholar
  11. 10.
    P. L. Chow, J. Math. Phys. 13, 1224 (1972); in Multiple Scattering and Waves in Random Media, eds. P. L. Chow, W. E. Kohler, G. C. Papanicolaou ( North Holland, Amsterdam, 1981 ), p. 89.MATHCrossRefGoogle Scholar
  12. 11.
    R. Dashen, J. Math. Phys. 20, 892 (1979); R. S. Patton, “Second Moments of the Pressure Field Near a Smooth Caustic,” in Adaptive Methods in Underwater Acoustics, ed. H. G. Urban (D. Reidel, Dordrecht, Holland, 1985 ).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1987

Authors and Affiliations

  • John R. Klauder
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA

Personalised recommendations