Spinless Relativistic Particle in the Presence of Minimal Uncertainty in the Momentum

Abstract

In this letter, we present the exact solution of the three-dimensional Klein–Gordon oscillator on the (anti)-de Sitter spaces, the energy spectrum and the associated wave functions are extracted and the wave functions are expressed according to the Jacobi polynomial. On the other hand, we have investigated the three-dimensional the Klein–Gordon equation with a Coulomb plus scalar potential, we use the perturbation theory to calculate corrections to the spectrum in this framework of the extended uncertainty principle.