### 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 GW^{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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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 443-470 |

Number of pages | 28 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E., & Yau, H. T. (2005). The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics. In

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 443-470). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_32