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We study the correction of the energy spectrum of a gravitational quantumwell due to the combined effect of the braneworld model with infinite extradimensions and generalized uncertainty principle. The correction terms arisefrom a natural deformation of a semiclassical theory of quantum gravitygoverned by the Schr\"odinger-Newton equation based on a minimal lengthframework. The two fold correction in the energy yields new values of thespectrum, which are closer to the values obtained in the GRANIT experiment.This raises the possibility that the combined theory of the semiclassicalquantum gravity and the generalized uncertainty principle may provide anintermediate theory between the semiclassical and the full theory of quantumgravity. We also prepare a schematic experimental set-up which may guide to theunderstanding of the phenomena in the laboratory.

Modification of Schr\"odinger-Newton equation due to braneworld models with minimal length