Advertisement

Theoretical and Mathematical Physics

, Volume 101, Issue 3, pp 1404–1412 | Cite as

Adelic model of harmonic oscillator

  • B. Dragovich
Article

Abstract

Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.

Keywords

Quantum Mechanic Harmonic Oscillator Uncertainty Relation Adelic Quantum Mechanic Adelic Model 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. V. Volovich,Class. Quantum Gravit.,4, 83 (1987).Google Scholar
  2. 2.
    P. G. O. Freund and E. Witten,Phys. Lett.,B199, 191 (1987).Google Scholar
  3. 3.
    I. Ya. Aref'eva, B. G. Dragović, and I. V. Volovich,Phys. Lett.,B209, 445 (1988);B212, 283,B214, 339.Google Scholar
  4. 4.
    V. S. Vladimirov,Lett. Math. Phys.,27, 123 (1993).Google Scholar
  5. 5.
    V. S. Vladimirov and I. V. Volovich,Dokl. Akad. Nauk SSSR,302, 320 (1988).Google Scholar
  6. 6.
    C. Alacoque, P. Ruelle, E. Thiran, D. Verstegen, and J. Weyers,Phys. Lett.,B211, 59 (1988).Google Scholar
  7. 7.
    V. S. Vladimirov and I. V. Volovich,Commun. Math. Phys.,123, 659 (1989).Google Scholar
  8. 8.
    V. S. Vladimirov and I. V. Volovich,Phys. Lett.,B217, 411 (1989).Google Scholar
  9. 9.
    Y. Meurice,Int. J. Mod. Phys.,A4, 5133 (1989).Google Scholar
  10. 10.
    E. I. Zelenov,Teor. Mat. Fiz.,80, 253 (1989).Google Scholar
  11. 11.
    V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov,Dokl. Akad. Nauk SSSR,310, 272 (1990);Izv. Akad. Nauk SSSR, Ser. Mat.,54, 275 (1990).Google Scholar
  12. 12.
    E. I. Zelenov,Teor. Mat. Fiz.,86, 375 (1991).Google Scholar
  13. 13.
    B. G. Dragović, P. H. Frampton, and B. V. Urošević,Mod. Phys. Lett.,A5, 1521 (1990); I. Ya. Aref'eva, B. G. Dargović, P. H. Frampton, and I. V. Volovich,Int. J. Mod. Phys.,A6, 4341 (1991).Google Scholar
  14. 14.
    V. S. Vladimirov,Usp. Mat. Nauk,43, 17 (1989).Google Scholar
  15. 15.
    A. Yu. Khrennikov,Usp. Mat. Nauk,45, 79 (1990).Google Scholar
  16. 16.
    B. G. Dragović,Teor. Mat. Fiz.,93, 211 (1992);J. Math. Phys.,34, 1143 (1993).Google Scholar
  17. 17.
    B. D. B. Roth,Phys. Lett.,B213, 263 (1988); M. D. MissarovPhys. Lett.,B272, 36 (1991).Google Scholar
  18. 18.
    W. H. Schikhof,Ultrametric Calculus, Cambridge Univ. Press, Cambridge (1984).Google Scholar
  19. 19.
    I. M. Gel'fand, M. I. Graev, and I. I. Piatetskii-Shapiro,Representation Theory and Automorphic Functions [in Russian], Nauka, Moscow (1966).Google Scholar
  20. 20.
    A. Yu. Khrennikov,J. Math. Phys.,32, 932 (1991).Google Scholar
  21. 21.
    V. S. Vladimirov and I. V. Volovich,Tr. Mat. Inst. Steklov,200, 88 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • B. Dragovich

There are no affiliations available

Personalised recommendations