Factorization in the quantum mechanics with the generalized uncertainty principle

Abstract

In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [(x) over cap, (p) over cap] = i (h) over bar (1 +alpha(p) over cap + beta(p) over cap (2) . 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.