Applications of the extended uncertainty principle in AdS and dS spaces

Hamil B., Merad M., Birkandan T.

European Physical Journal Plus, vol.134, no.6, 2019 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 134 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1140/epjp/i2019-12633-y
  • Title of Journal : European Physical Journal Plus


.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.