Communications in Mathematical Physics

, Volume 44, Issue 2, pp 129–132 | Cite as

Uncertainty relations for information entropy in wave mechanics

  • Iwo Białynicki-Birula
  • Jerzy Mycielski


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.


Entropy Neural Network Statistical Physic Probability Distribution Complex System 
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  1. 1.
    Babenko, K.I.: Izv. Akad. Nauk SSSR. Ser. Mat.25, 531 (1961)Google Scholar
  2. 2.
    Beckner, W.: Proc. Nat. Acad. Sci. U.S.A.72, 638 (1975)Google Scholar
  3. 3.
    Gross, L.: Logarithmic Sobolev Inequalities (to appear in Amer. J. of Math)Google Scholar
  4. 4.
    Bialynicki-Birula, I., Mycielski, J.: Wave equations with logarithmic nonlinearities. Bull. Acad. Polon. Sci. Cl. III.23, 461 (1975)Google Scholar
  5. 5.
    Zygmund, A.: Trigonometric series, Vol. II, p. 101. Cambridge University Press 1959Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Iwo Białynicki-Birula
    • 1
    • 2
  • Jerzy Mycielski
    • 1
  1. 1.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland
  2. 2.Department of PhysicsUniversity of PittsburghPittsburghUSA

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