Quantifying the failure of Schrödinger dynamics in the free expansion of relativistic particles

Regular Article


It is known that the Schrödinger equation fails in describing the dynamics of highly energetic particles. We propose to quantify this lack of Lorentz covariance by evaluating the probability of a particle to be measured outside the set of light cones which are compatible with its initial wave function. We consider a simple case of a particle released from a box, which, in turn, is inside a larger container. It is shown that besides the increasing error at relativistic energies, there may be a complete breakdown, with Schrödinger dynamics allowing for deterministic, superluminal signaling for Lorentz factors above 129. In addition, we give an exact asymptotic expression for the violation in local causality by employing the stationary exponent method, from which the Compton wave length of the particle naturally arises as the relevant scale for the stationary points.


  1. 1.
    E. Fermi, Phys. Rev. 75, 1169 (1949)ADSCrossRefGoogle Scholar
  2. 2.
    S.M. Ulam, Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics, and Probability, Berkeley, 1960, edited by J. Neyman, Vol. 3 (University of California Press, Berkeley, 1961)Google Scholar
  3. 3.
    S.R. Jain, Phys. Rev. Lett. 70, 3553 (1993)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    A.J. Makowski, S.T. Dembiński, Phys. Lett. A 154, 217 (1991)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    S.V. Mousavi, Phys. Lett. A 377, 1513 (2013)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    S.V. Mousavi, EPL 99, 30002 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    C. Aslangul, J. Phys. A: Math. Theor. 41, 1 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Styer, Am. J. Phys. 69, 56 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions (Dover, New York, 1965)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal de PernambucoRecifeBrazil

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