In this work, we explore the de Broglie-Bohm quantum cosmology for a stiff matter, \(p=\rho \) , anisotropic n-dimensional Universe. One begins by considering a Gaussian wave function for the Universe, which depends on the momenta parameters \(q_1\) and \(q_2\) , in addition to the dispersion parameters \(\sigma _1\) and \(\sigma _2\) . Our solutions show that the extra dimensions are stabilized through a dynamical compactification mechanism within the quantum cosmology framework. In this case, we find two distinct configurations for the dynamics of the extra dimensions. The first configuration features larger extra dimensions at the bounce, which subsequently undergo compactification to a smaller size. In contrast, the second configuration exhibits a smaller extra dimension at the bounce, evolving toward a larger, finite, and stabilized value. We also address the particular five-dimensional case where the Wheeler-DeWitt equation degenerates.
