  We study the correction of the energy spectrum of a gravitational quantum
well due to the combined effect of the braneworld model with infinite extra
dimensions and generalized uncertainty principle. The correction terms arise
from a natural deformation of a semiclassical theory of quantum gravity
governed by the Schr\"odinger-Newton equation based on a minimal length
framework. The two fold correction in the energy yields new values of the
spectrum, which are closer to the values obtained in the GRANIT experiment.
This raises the possibility that the combined theory of the semiclassical
quantum gravity and the generalized uncertainty principle may provide an
intermediate theory between the semiclassical and the full theory of quantum
gravity. We also prepare a schematic experimental set-up which may guide to the
understanding of the phenomena in the laboratory.
