Skip to main content
SpringerLink
Log in

Uncertainty relations for information entropy in wave mechanics

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

Abstract

New uncertainty relations in quantum mechanics are derived. They express restrictions imposed by quantum theory on probability distributions of canonically conjugate variables in terms of corresponding information entropies. The Heisenberg uncertainty relation follows from those inequalities and so does the Gross-Nelson inequality.

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. Babenko, K.I.: Izv. Akad. Nauk SSSR. Ser. Mat.25, 531 (1961)

    Google Scholar 

  2. Beckner, W.: Proc. Nat. Acad. Sci. U.S.A.72, 638 (1975)

    Google Scholar 

  3. Gross, L.: Logarithmic Sobolev Inequalities (to appear in Amer. J. of Math)

  4. Bialynicki-Birula, I., Mycielski, J.: Wave equations with logarithmic nonlinearities. Bull. Acad. Polon. Sci. Cl. III.23, 461 (1975)

    Google Scholar 

  5. Zygmund, A.: Trigonometric series, Vol. II, p. 101. Cambridge University Press 1959

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Warsaw University, 00-681, Warsaw, Poland

    Iwo Białynicki-Birula & Jerzy Mycielski

  2. Department of Physics, University of Pittsburgh, Pittsburgh, USA

    Iwo Białynicki-Birula

Authors
  1. Iwo Białynicki-Birula
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy Mycielski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. Haag

Research partly supported by the NSF Grant 36217.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Białynicki-Birula, I., Mycielski, J. Uncertainty relations for information entropy in wave mechanics. Commun.Math. Phys. 44, 129–132 (1975). https://doi.org/10.1007/BF01608825

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01608825

Keywords

Search

Navigation