  More recently, we have proposed a set of noncommutative space that describes
the quantum gravity at the Planck scale (J. Phys. A: Math. Theor53, 115303
(2020)). The interesting significant result, we found is that, the generalized
uncertainty principle induced a maximal measurable length of quantum gravity.
This measurement revealed strong quantum gravitational effects at this scale
and predicted the measurement of gravity particles with low energies. In the
present paper, to make an evidence this prediction, we study in this space, the
dynamics of a particle with position-dependent mass (PDM) trapped in an
infinite square well. We show that, by increasing the quantum gravitational
effect, the PDM of the particle increases and induces contractions of the
quantum energy levels. These contractions are more pronounced as one increases
the quantum levels, allowing the particle to jump from one state to another
with low energies and with high probability densities. Moreover, with the
spectrum of this system at hand, we develop generalized coherent states based
on the Gazeau-Klauder formalism. These states are shown to satisfy the
Klauder's minimum conditions. Some statistical properties are calculated and
analyzed. We find that these states are sub-Poissonian in nature.
