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We discuss an effective theory for the quantum static gravitational potentialin spherical symmetry up to the first post-Newtonian correction. We build asuitable Lagrangian from the weak field limit of the Einstein-Hilbert actioncoupled to pressureless matter. Classical solutions of the field equation leadto the correct post-Newtonian expansion. Furthermore, we portray the Newtonianresults in a quantum framework by means of a coherent quantum state, which isproperly corrected to accomodate post-Newtonian corrections. Theseconsiderations provide a link between the corpuscular model of Dvali and Gomezand standard post-Newtonian gravity, laying the foundations for futureresearch.

Quantum post-Newtonian theory for corpuscular Black Holes