Foundations of Physics Letters

, Volume 7, Issue 5, pp 419–436 | Cite as

Can an observable with discrete eigenvalues be conjugate to a continuum observable?

  • R. T. Deck
  • N. Öztürk


We point out that, in combination with the normalization and completeness relations for the eigenkets of the operators, the commutation relation [Oα, Oβ]=±ih places severe restrictions on the eigenvalues of the two operators Oα and Oβ. These restrictions can be used both to determine the character of the pairs of conjugate observables that can be involved in uncertainty relations and to predict thequantized form of the eigenvalues of a discrete observable which is conjugate to a continuum observable with a finite spectrum.

Key words

quantum mechanics conjugate observables angular-momentum quantization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. P. Robertson,Phys. Rev. 34, 163 (1929).Google Scholar
  2. 2.
    P. Jordan,Z. Phys. 44, 1 (1927).Google Scholar
  3. 3.
    D. Judge,Phys. Lett. 5, 189 (1964);Nuovo Cimento 31, 332 (1964).Google Scholar
  4. 4.
    R. Jackiw,J. Math. Phys. 9, 339, (1968).Google Scholar
  5. 5.
    P. Carruthers and M. M. Nieto,Rev. Mod. Phys. 40, 411 (1968).Google Scholar
  6. 6.
    D. Deutsch,Phys. Rev. Lett. 50, 631 (1983); M. H. Partovi,Phys. Rev. Lett. 50, 1883 (1983).Google Scholar
  7. 7.
    E. Breitenberger,Found. Phys. 15, 353 (1985).Google Scholar
  8. 8.
    P. A. M. Dirac,The Principles of Quantum Mechanics, 4th edn. (Clarendon, Oxford, 1958).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • R. T. Deck
    • 1
  • N. Öztürk
    • 1
  1. 1.Department of Physics and AstronomyUniversity of ToledoToledo

Personalised recommendations