  We study an effective quantum description of the static gravitational
potential for spherically symmetric systems up to the first post-Newtonian
order. We start by obtaining a Lagrangian for the gravitational potential
coupled to a static matter source from the weak field expansion of the
Einstein-Hilbert action. By analysing a few classical solutions of the
resulting field equation, we show that our construction leads to the expected
post-Newtonian expressions. Next, we show that one can reproduce the classical
Newtonian results very accurately by employing a coherent quantum state and
modifications to include the first post-Newtonian corrections are considered.
Our findings establish a connection between the corpuscular model of black
holes and post-Newtonian gravity, and set the stage for further investigations
of these quantum models.
