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Applications of the extended uncertainty principle in AdS and dS spaces

  • B. Hamil
  • M. MeradEmail author
  • T. Birkandan
Regular Article
  • 30 Downloads

Abstract.

All commutation relations are modified in (anti)-de Sitter background and the Heisenberg uncertainty principle is changed to the so-called extended uncertainty principle (EUP). In this scenario, the commutators between position and momentum operators are functions of the position space variables, instead of a constant and the coordinate representation of the momentum operators for this model becomes coordinate dependent. In the AdS space, a lower bound on momentum uncertainty arises, which is not present in the dS space. In this paper, we present an exact solution of the D -dimensional free particle, the harmonic oscillator and pseudoharmonic oscillator in AdS and dS spaces. The eigenfunctions are determined for both cases and the energy eigenvalues are obtained.

References

  1. 1.
    H.S. Snyder, Phys. Rev. 71, 38 (1947)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    H.S. Snyder, Phys. Rev. 72, 68 (1947)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Kontsevich, Lett. Math. Phys. 66, 157 (2003)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Kowalski-Glikmanand, S. Nowak, Int. J. Mod. Phys. D 13, 299 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    S. Mignemi, Phys. Lett. B 672, 186 (2009)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    P. Pedram, Phys. Lett. B 702, 295 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    P.A.M. Dirac, Ann. Math. 35, 657 (1935)CrossRefGoogle Scholar
  8. 8.
    S. Mignemi, Ann. Phys. 522, 924 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Han-ying Guo, Chao-guang Huang, Yu Tian, Zhan Xu, Bin Zhou, Front. Phys. China 2, 358 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    S. Mignemi, Mod. Phys. Lett. A 25, 1697 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    B. Hamil, M. Merad, Int. J. Mod. Phys. A 33, 1850177 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    B. Hamil, M. Merad, Eur. Phys. J. Plus 133, 174 (2018)ADSCrossRefGoogle Scholar
  13. 13.
    W.S. Chung, H. Hassanabadi, Mod. Phys. Lett. A 32, 1750138 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    W.S. Chung, H. Hassanabadi, J. Korean Phys. Soc. 71, 13 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    W.S. Chung, H. Hassanabadi, Phys. Lett. B 785, 127 (2018)ADSCrossRefGoogle Scholar
  16. 16.
    W.S. Chung, H. Hassanabadi, Mod. Phys. Lett. A 33, 1850150 (2018)ADSCrossRefGoogle Scholar
  17. 17.
    S. Ghosh, S. Mignemi, Int. J. Theor. Phys. 50, 1803 (2011)CrossRefGoogle Scholar
  18. 18.
    B. Mirza, M. Zarei, Phys. Rev. D 79, 125007 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    N. Messai, B. Hamil, A. Hafdallah, Mod. Phys. Lett. A 33, 1850202 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    C. Dullemond, E. van Beveren, J. Math. Phys. 26, 2050 (1985)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    S.Yu. Slavyanov, W. Lay, Special Functions: A Unified Theory Based on Singularities (Oxford University Press, New York, 2000)Google Scholar
  22. 22.
    S. Mignemi, Class. Quantum Grav. 29, 215019 (2012)CrossRefGoogle Scholar
  23. 23.
    L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Phys. Rev. D 65, 125027 (2002)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    I.I. Gol'dman, V.D. Krivchenkov, V.I. Kogan, V.M. Galitskii, Problems in Quantum Mechanics (Academic Press, New York, 1960)Google Scholar
  25. 25.
    S.H. Dong, J. Phys. A: Math. Gen. 36, 4977 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    S. Ikhdair, R. Sever, J. Mol. Struct. Theochem. 806, 155 (2007)CrossRefGoogle Scholar
  27. 27.
    S.H. Dong, D. Morales, J. García-Ravelo, Int. J. Mod. Phys. E 16, 189 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    S. Flugge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1994)Google Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département de TC de SNVUniversité Hassiba BenboualiChlefAlgeria
  2. 2.Département des Sciences de la Matière, Faculté des Sciences ExactesUniversité de Oum El BouaghiOum El BouaghiAlgeria
  3. 3.Department of PhysicsIstanbul Technical UniversityIstanbulTurkey

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