The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

Starting with a “relativistic” Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle numberN→∞ and the gravitation constantG→0 we obtain the well known semiclassical theory for the ground state of stars. For fermions, the correct limit is to fixGN2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fixGN 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.

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