### 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) |
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Pages (from-to) | 147-174 |

Number of pages | 28 |

Journal | Communications In Mathematical Physics |

Volume | 112 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1987 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E., & Yau, H. T. (1987). The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics.

*Communications In Mathematical Physics*,*112*(1), 147-174. https://doi.org/10.1007/BF01217684