Starting with a “relativistic” Schrodinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N → ∞ and the gravitation constant G → 0 we obtain the well known semiclassical theory for the ground state of stars. For fermions; the correct limit is to fix GN 2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution — a fact which had not been established previously.