  We analyse the classical configurations of a bootstrapped Newtonian potential
generated by homogeneous spherically symmetric sources in terms of a quantum
coherent state. We first compute how the mass and mean wavelength of these
solutions scale in terms of the number of quanta in the coherent state. We then
note that the classical relation between the ADM mass and the proper mass of
the source naturally gives rise to a Generalised Uncertainty Principle for the
size of the gravitational radius in the quantum theory. Consistency of the mass
and wavelength scalings with this GUP requires the compactness remains at most
of order one even for black holes, and the corpuscular predictions are thus
recovered, with the quantised horizon area expressed in terms of the number of
quanta in the coherent state. Our findings could be useful for analysing the
classicalization of gravity in the presence of matter and the avoidance of
singularities in the gravitational collapse of compact sources.
