Applications of the extended uncertainty principle in AdS and dS spaces

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.

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Hamil, B., Merad, M. & Birkandan, T. Applications of the extended uncertainty principle in AdS and dS spaces. Eur. Phys. J. Plus 134, 278 (2019). https://doi.org/10.1140/epjp/i2019-12633-y

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