Skip to main content
SpringerLink
Log in

Monodromy in the quantum spherical pendulum

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this article we show that monodromy in the quantum spherical pendulum can be interpreted as a Maslov effect: i.e. as multi-valuedness of a certain generating function of the quantum energy levels.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cushman, R., Duistermaat, J. J.: preprint (1988)

  2. Duistermaat, J. J.: On the existence of global action-angle variables. Commun. Pure Appl. Math.33, 687–706 (1980)

    Google Scholar 

  3. Duistermaat, J. J., Guillemin, V.: The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math.29, 184–269 (1975)

    Google Scholar 

  4. Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. New York: Cambridge University Press 1985

    Google Scholar 

  5. Guillemin, V., Sternberg, S.: Homogeneous quantization and multiplicities of group representations. J. Funct. Anal.47, 344–380 (1982)

    Google Scholar 

  6. Guillemin, V., Uribe, A.: Circular symmetry and the trace formula, preprint (1988)

  7. Hörmander, L.: Fourier integral operators I. Acta Math.129, 79–183 (1971)

    Google Scholar 

  8. Weinstein, A.: Lectures on Symplectic Manifolds, CBMS Reg. Conf. Ser. Math., vol29, Providence, R.I.: A.M.S. 1977

    Google Scholar 

  9. Weinstein, A. Symplectic Geometry. In: Symposium on the Mathematical Heritage of Poincaré. Providence, R. I.: A.M.S. 1983

    Google Scholar 

  10. Weinstein, A.: Symplectic Geometry. Bull. Am. Math. Soc.5, 1–13 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, M.I.T., 02139, Cambridge, MA, USA

    V. Guillemin

  2. Mathematics Department, Princeton University, 08544, Princeton, NJ, USA

    A. Uribe

Authors
  1. V. Guillemin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Uribe
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guillemin, V., Uribe, A. Monodromy in the quantum spherical pendulum. Commun.Math. Phys. 122, 563–574 (1989). https://doi.org/10.1007/BF01256493

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01256493

Keywords

Search

Navigation