Abstract
In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [Formula: see text]. For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.
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