Quantum Integrability

Reichl, L. E.

doi:10.1007/978-1-4757-4352-4_5

L. E. Reichl²

Part of the book series: Institute for Nonlinear Science ((INLS))

217 Accesses

Abstract

As we have seen in Sect. (2.3.1), a classical conservative system with N degrees of freedom is integrable if there exist N independent global functions whose mutual Poisson brackets vanish. Integrability in quantum systems is defined in an analogous manner.

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)

eBook: USD 74.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Atkins, P.W., Child, M.S., and Phillips, C.S.G., Tables for Group Theory(Oxford University Press, 1970).
Google Scholar
Eckhardt, B. (1988): Phys. Rept. 163205.
Article MathSciNet ADS Google Scholar
Ganoulis, N. (1987): Commun.in Math.Phys. 10923.
Article MathSciNet ADS MATH Google Scholar
Gutzwiller, M.C. (1980): Annals of Physics 124347.
Article MathSciNet ADS Google Scholar
Gutzwiller, M.C. (1981): Annals of Physics 133304.
Article MathSciNet ADS Google Scholar
Hietarinta, J. (1982): Phys. Lett. A9355 (1982).
Article MathSciNet Google Scholar
Hietarinta, J. (1984): J. Math. Phys. 251833.
Article MathSciNet ADS Google Scholar
Holt, C.R. (1982): J. Math. Phys. 231037.
Article MathSciNet ADS MATH Google Scholar
Magyari, E., Thomas, H., Weber, R., Kaufman, C., and Muller, G. (1987): Z. Phys. B. — Condensed Matter 65363.
Article MathSciNet ADS Google Scholar
Mansfield, P. (1982): Nuclear Phys. B208277.
Article MathSciNet ADS Google Scholar
Moser, J. (1979): Amer. Sci. (USA) 67689.
ADS Google Scholar
Olive, D.I. and Turok, N. (1983a): Nue. Phys. B215470.
Article MathSciNet ADS Google Scholar
Olive, D.I. and Turok, N. (1983b): Nue. Phys. B220491.
Article MathSciNet ADS Google Scholar
Olshanetsky, M.A. and Perelomov, A.M. (1983): Phys. Repts. 94313.
Article MathSciNet ADS Google Scholar
Srivastava, N., Kaufman, C., Müller, G., Weber, R., and Thomas, H., (1988): Z. Phys. B.- Condensed Matter 70251.
Article ADS Google Scholar
Srivastava, N., Kaufman, C., Müller, G. (1990a): J. Applied Phys.675627.
Article ADS Google Scholar
Srivastava, N. and Müller, G. (1990b): Z. Phys. B80137.
Article Google Scholar
Müller, G. (1986): Phys. Rev. A343345.
Article MathSciNet Google Scholar
Peres, A. (1984): Phys. Rev. Lett. 531711.
Article ADS Google Scholar
Zaslavsky, G.M. (1981): Phys. Repts. 80157.
Article MathSciNet ADS Google Scholar

Download references

Author information

Authors and Affiliations

Center for Statistical Mechanics and Complex Systems, Department of Physics, University of Texas at Austin, Austin, TX, 78172, USA
L. E. Reichl

Authors

L. E. Reichl
View author publications
You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Reichl, L.E. (1992). Quantum Integrability. In: The Transition to Chaos. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4352-4_5

Download citation

DOI: https://doi.org/10.1007/978-1-4757-4352-4_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-4354-8
Online ISBN: 978-1-4757-4352-4
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics