Foundations of Physics

, Volume 20, Issue 10, pp 1233–1240 | Cite as

Quantum theory of single events: Localized De Broglie wavelets, Schrödinger waves, and classical trajectories

  • A. O. Barut
Part I. Invited Papers Dedicated To John Stewart Bell


For an arbitrary potential V with classical trajectoriesx=g(t), we construct localized oscillating three-dimensional wave lumps ψ(x, t,g) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbitg(t), slightly modified due to the potential V, and ψ(x, t,g) satisfies the Schrödinger equation. The field energy, momentum, and angular momentum calculated as integrals over all space are equal to the particle energy, momentum, and angular momentum. The relation to coherent states and to Schrödinger waves is also discussed.


Angular Momentum Crest Quantum Theory Potential Versus Coherent State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Born,Z. Phys. 37, 863 (1926;38, 803 (1926.)Google Scholar
  2. 2.
    A. O. Barut,Phys. Lett. A 143, 349 (1990).Google Scholar
  3. 3.
    A. O. Barut and A. Grant,Found. Phys. Lett. 3, 303 (1990).Google Scholar
  4. 4.
    For a historical discussion, see A. O. Barut, “Louis de Broglie and the single quantum particle,” in L. de Broglie,Heisenberg's Uncertainties and the Probabilistic Interpretation of Wave Mechanics, translation by A. van der Merwe (Kluwer, Dordrecht, 1990).Google Scholar
  5. 5.
    E. Schrödinger,Naturwissenschaften 14, 664 (1926).Google Scholar
  6. 6.
    The distinction between ψ(x,t;g) and ψ(x,t) is discussed in A. O. Barut,Found. Phys. Lett. 1, 47 (1988) and Ref. 4, and the passage from one to the other in A. O. Barut, in “Symposium on the Foundations of Modern Physics 1990” (Joensuu, Finland), World Scientific.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • A. O. Barut
    • 1
  1. 1.International Centre for Theoretical PhysicsTrieste-MiramareItaly

Personalised recommendations