Skip to main content
SpringerLink
Log in

Classical Interpretation of a Deformed Quantum Oscillator

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Following the same procedure that allowed Shcrödinger to construct the (canonical) coherent states in the first place, we investigate on a possible classical interpretation of the deformed harmonic oscillator. We find that, these oscillator, also called q-oscillators, can be interpreted as quantum versions of classical forced oscillators with a modified q-dependant frequency.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Arik, M., Coon, D.D.: Hilbert spaces of analytic functions and generalized coherent states. J. Math. Phys. 17, 524 (1976)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Biedenharn, L.C.: The quantum group \(SU_q(2)\) and a q-analogue of the boson operators. J. Phys. A 22, L873 (1989)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. Macfarlane, A.J.: On q-analogues of the quantum harmonic oscillator and the quantum group \(SU_q(2)\). J. Phys. A 22, 4581 (1989)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Klauder, J.R.: Continuous representation theory. I. Postulates of continuous representation theory. J. Math. Phys. 4, 1055 (1963)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Klauder, J.R.: Generalized relation between quantum and classical dynamics. J. Math. Phys. 4, 1058 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  6. Klauder, J.R., Skagerstam, B.S.: Coherent States, Applications in Physics and Mathematical Physics, p. 991. World Scientific, Singapore (1985)

    Book  MATH  Google Scholar 

  7. Drinfeld, V. G., Quantum Groups dans.: Proceedings of the International Congress of Mathematicians, Berkeley 1986, p. 798. AMS (1987)

  8. Jimbo, M.: A q-difference analogue of U(g) and the Yang–Baxter equation. Lett. Math. Phys. 10, 63 (1985)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Glauber, R.: The quantum theory of optical coherence. Phys. Rev. 130, 2529 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  10. Greenberg, O.W.: Example of infinite statistics. Phys. Rev. Lett. 64, 705 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. Schrödinger, E.: Naturwissenscahften 14, 664 (1926)

    Article  ADS  MATH  Google Scholar 

  12. Ali, S.T., Antoine, J.-P., Gazeau, J.-P.: Coherent States, Wavelets and Their Generalizations. Springer-Verlag, New York (2000)

    Book  MATH  Google Scholar 

  13. Daskaloyannis, C.: Generalized deformed oscillator and nonlinear algebras. J. Phys. A24, L789 (1991)

    ADS  MathSciNet  Google Scholar 

  14. Gazeau, J.P., Champagne, B.: The Fibonnaci-deformed harmonic oscillator in Algbraic methods in physics CRM series in Theoretical and Mathematical Physics. Spinger-Verlag, Berlin (2001)

    Google Scholar 

  15. El Baz, M., Hassouni, Y.: Special deformed exponential functions leading to more consistent Klauder’s coherent states. Phys. Lett. A300, 361 (2002)

    Article  ADS  Google Scholar 

  16. Perelomov, A.M.: On the completeness of some subsystems of q-deformed coherent states. Helv. Phys. Acta 68, 554 (1996)

    MathSciNet  Google Scholar 

  17. El Baz, M., Hassouni, Y., Madouri, F.: New construction of coherent states for generalized harmonic oscillators. Rep. Math. Phys. 50, 263 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. Klauder, J.R., Penson, K.A., Sixdeniers, J.-M.: Constructing coherent states through solutions of Stieltjes and Hausdorff moment problem. Phys. Rev. A64, 13817 (2001)

    Article  ADS  Google Scholar 

  19. Penson, K.A., Solomon, A.I.: New generalized coherent states. J. Math. Phys. 40, 2354 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. Gazeau, J.-P., Klauder, J.R.: Coherent states for systems with discrete and continuous spectrum. J. Phys. A 32, 123 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, LPT-URAC 13, Faculté des Sciences, Université Mohamed V-Agdal, B.P 1014, Av.Ibn Battouta, Agdal, Rabat, Morocco

    J. Batouli & M. El Baz

Authors
  1. J. Batouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. El Baz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. El Baz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Batouli, J., El Baz, M. Classical Interpretation of a Deformed Quantum Oscillator. Found Phys 44, 105–113 (2014). https://doi.org/10.1007/s10701-013-9766-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-013-9766-9

Keywords

Search

Navigation