Abstract
Starting with a “relativistic” Schrödinger 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.
Dedicated to Walter Thirring on hid 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. (2001). The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_32
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