Skip to main content
SpringerLink
Log in

Lecture 16: Semiclassical Approximation for Fast Oscillating Phases. Stationary Phase. W.K.B. Method. Semiclassical Quantization Rules

  • Chapter
  • First Online:
Lectures on the Mathematics of Quantum Mechanics I

Part of the book series: Atlantis Studies in Mathematical Physics: Theory and Applications ((ASMPTA,volume 1))

  • 2444 Accesses

Abstract

We make in this Lecture an analysis of the semiclassical approximation for states represented in configuration space by wave function with fast oscillating phase.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Berry, M., & Mount, K. (1972). Reports on Progress in Physics, 35, 315–397.

    Google Scholar 

  2. Combescure, M., & Robert, D. (2012). Coherent states. Dordrecht: Springer.

    Google Scholar 

  3. Duistermaat, J. J. (1974). Communications on Pure and Applied Mathematics, 27, 207–281.

    Google Scholar 

  4. Evans, L. (1998). PDE, Graduate studies in mathematics. Providence: AMS.

    Google Scholar 

  5. Fedoryiuk, M. (1999). P.D.E. Encyclopedia of mathematical sciences (Vol. 34). New York: Springer.

    Google Scholar 

  6. Fujiwara, D. (1980). Duke Mathematical Journal, 47, 559–600.

    Google Scholar 

  7. Frohman, N., & Frohman, P. O. (1965). J.W.K.B. approximation, Amsterdam: North-Holland.

    Google Scholar 

  8. Gutzwiller, M. (1967). Journal of Mathematical Physics, 8, 1979–2000.

    Google Scholar 

  9. Heading, J. (1962). An Introduction to Phase-space Methods, London: Methuen.

    Google Scholar 

  10. Hormander, L. (1967). Pseudodifferential operators and hypoelliptic equations. Proceedings of the Symposium Pure and Applied Mathematics, 10, 138–183.

    Google Scholar 

  11. Keller, J. (1958). Annals of Physics, 4, 180–188.

    Google Scholar 

  12. Maslov, V. (1994). The complex W.K.B. method, Progress in physics N.16, Basil: Birkhauser.

    Google Scholar 

  13. Voros, A. (1989). Physical Review A, 49, 6814–6825.

    Google Scholar 

  14. Wittaker, E., & Watson, G. (1946). A course of modern analysis. Cambridge: Cambridge University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Università Sapienza, Rome, Italy

    Gianfausto Dell’Antonio

  2. Mathematics Area, SISSA, Trieste, Italy

    Gianfausto Dell’Antonio

Authors
  1. Gianfausto Dell’Antonio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gianfausto Dell’Antonio .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Atlantis Press and the author(s)

About this chapter

Cite this chapter

Dell’Antonio, G. (2015). Lecture 16: Semiclassical Approximation for Fast Oscillating Phases. Stationary Phase. W.K.B. Method. Semiclassical Quantization Rules. In: Lectures on the Mathematics of Quantum Mechanics I. Atlantis Studies in Mathematical Physics: Theory and Applications, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-118-5_16

Download citation

Publish with us

Policies and ethics

Search

Navigation