Abstract
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 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.
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Communicated by E.H. Lieb
Dedicated to Walter Thirring on his 60th birthday
Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A01
Work supported by Alfred Sloan Foundation dissertation Fellowship
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Lieb, E.H., Yau, HT. The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics. Commun.Math. Phys. 112, 147–174 (1987). https://doi.org/10.1007/BF01217684
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DOI: https://doi.org/10.1007/BF01217684