https://doi.org/10.1140/epjp/i2019-12633-y
Regular Article
Applications of the extended uncertainty principle in AdS and dS spaces
1
Département de TC de SNV, Université Hassiba Benbouali, Chlef, Algeria
2
Département des Sciences de la Matière, Faculté des Sciences Exactes, Université de Oum El Bouaghi, 04000, Oum El Bouaghi, Algeria
3
Department of Physics, Istanbul Technical University, 34469, Istanbul, Turkey
* e-mail: meradm@gmail.com
Received:
11
February
2019
Accepted:
17
March
2019
Published online:
21
June
2019
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.
© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019
