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The Chandrasekhar theory of stellar collapse as the limit quantum mechanics. (English) Zbl 0641.35065

Summary: Starting with a “relativistic” Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle number \(N\to \infty\) and the gravitation constant \(G\to 0\) 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.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
82B10 Quantum equilibrium statistical mechanics (general)
85A15 Galactic and stellar structure
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