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

Elliott H. Lieb; Horng Tzer Yau

doi:10.1007/BF01217684

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

Elliott H. Lieb, Horng Tzer Yau

Mathematics

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266 Scopus citations

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.

Original language	English (US)
Pages (from-to)	147-174
Number of pages	28
Journal	Communications In Mathematical Physics
Volume	112
Issue number	1
DOIs	https://doi.org/10.1007/BF01217684
State	Published - Mar 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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AU - Yau, Horng Tzer

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N2 - 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 GN2/3 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.

AB - 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 GN2/3 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.

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

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