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 constantG0 we obtain the well known semiclassical theory for the ground state of stars. For fermions, the correct limit is to fixGN ^2/3 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.Dedicated to Walter Thirring on his 60^th birthdayWork partially supported by U.S. National Science Foundation grant PHY 85-15288-A01Work supported by Alfred Sloan Foundation dissertation Fellowship