Skip to main content
SpringerLink
Log in

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The stochastic quantization method recently developed by Haba and Kleinert is extended to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. Using a rescaling transformation, the Schrö-din-ger equation for the time-dependent harmonic oscillator is obtained after averaging of a classical stochastic differential equation.

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

  • Bacciagaluppi, G. (1999). Foundations of Physics Letters 12, 1.

    Google Scholar 

  • Belavkin, V. P. (2003). International Journal of Theoretical Physics 42, 2461.

    Google Scholar 

  • Damgaard, P. H. and Hüffel, H. (1987). Physics Reports 152, 227.

    CAS  Google Scholar 

  • de la Peña, L. and Cetto, A. M. (1996). The Quantum Dice, Kluwer, Dordretch, Netherlands.

    Google Scholar 

  • Espinoza, P. (2000). Ermakov-Lewis Dynamic Invariants with Some Applications. ArXiv: math-ph/ 0002005.

  • Gaioli, F. H., Garcia Alvarez, E. T, and Guevara, J. (1997). International Journal of Theoretical Physics 36, 2167.

    Google Scholar 

  • Haas, F. and Goedert, J. (1999). Journal of Physics A: Mathematics and Generalities 32, 6837.

    Google Scholar 

  • Haas, F. (2002). Physical Review A 65, 33603.

    Google Scholar 

  • Haba Z. and Kleinert, H. (2002). Physics Letters A 294, 139.

    CAS  Google Scholar 

  • Hooft, G. ‘t. (1997). Foundations of Physics Letters 10, 105.

    Google Scholar 

  • Lewis, H. R. (1967). Physical Review Letters, 18, 510.

    CAS  Google Scholar 

  • Lewis, H. R. and Riesenfeld, W. B. (1969). Journal of Mathematical Physics 10, 1458.

    Google Scholar 

  • Munier, A., Burgan, J. R., Feix, M. R, and Fijalkow, E. (1981). Journal of Mathematical Physics 22, 1219.

    Google Scholar 

  • Namiki, N. (1982). Stochastic Quantization, Springer-Verlag, Heidelberg, Germany.

    Google Scholar 

  • Namiki, M. (2000). Acta Applicandae Mathematicae 63, 275.

    Google Scholar 

  • Nelson, E. (1967). Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, USA.

    Google Scholar 

  • Olavo, L. S. F. (2000). Physical Review A 61, 052109.

    Google Scholar 

  • Parisi, G. and Wu, Y. S. (1982). Science Sinica 24, 483.

    Google Scholar 

  • Pinney, E. (1950). Proceedings of the American Mathematical Society 1, 681.

  • Torres Jr., M. S. and Figueiredo, J. M. A. (2003). Physica A 329, 68.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidade do Vale do Rio dos Sinos, Ciências Exatas e Tecnológicas Av. UNISINOS, 950., 93022-000, São Leopoldo, RS, Brazil

    F. Haas

Authors
  1. F. Haas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Haas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haas, F. Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method. Int J Theor Phys 44, 1–9 (2005). https://doi.org/10.1007/s10773-005-1429-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-005-1429-y

KEY WORDS

Search

Navigation