  We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in
the presence of the minimal length uncertainty and the maximal momentum. This
form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with
various theories of quantum gravity and predicts a minimal length uncertainty
proportional to $\hbar\sqrt{\beta}$ and a maximal momentum proportional to
$1/\sqrt{\beta}$, where $\beta$ is the deformation parameter. We also find the
semiclassical energy spectrum and discuss the effects of this GUP on the
transition rate of the ultra cold neutrons in gravitational spectrometers.
Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound
on the dimensionless GUP parameter.
